Rebound surface hardness and related properties of concrete

BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS Department of Construction Materials and Engineering Geology

Rebound surface hardness

and related properties of concrete

PhD THESIS Katalin Szilágyi

MSc (CE)

S u p e r v i s o r István Zsigovics PhD, MSc (CE)

Budapest , 2013

Contents

Summary ^V

Notations VI

Glossary ^VIII

1. Introduction

1.1 Scientific background 1.2 Research significance 1.3 Objectives

1 4 4

2. Literature review

2.1 Historical overview

2.2 Contact mechanical interpretation of hardness 2.3. Types of rebound hammers

2.3.1 Leeb hardness tester 2.3.2 Rebound hammers

2.4 Operating principle of the rebound hammer 2.5 Impact phenomena of the rebound hammer test

2.5.1 Theoretical considerations

2.5.2 Experimental results for the stress wave propagation 2.6 Parameters influencing the rebound index

2.6.1 Effects by the device

2.6.2 Effects by the concrete structure

2.7 Variability parameters of rebound surface hardness 2.8 Number of repetition of rebound index readings

2.9 Outputs of rebound hardness test – establishing the strength relationships 2.10 Regression analysis of compressive strength and rebound hardness 2.11 Standardization of in-situ strength estimation by the rebound method

2.11.1 Improvement of the reliability of the strength estimation 2.11.2 U.S. practice

2.11.3 European practice 2.11.4 Hungarian practice

2.11.5 Conclusions on standardization

5 9 10 11 12 12 14 14 17 18 18 19 21 23 24 25 28 28 29 29 30 35

3. Research methodology

3.1 Statistical analysis 3.1.1 Normality tests

3.1.2 Calculation of repeatability parameters 3.1.3 Goodness of fit tests

3.1.4 Influences on the repeatability parameters

37

37

38

38

39

3.2 Modelling

3.2.1 Development of the phenomenological model 3.2.2 Robustness study by parametric simulation 3.2.3 Model verification with laboratory tests 3.3 Targeted experiments

3.3.1 Scope of study 3.3.2 Test parameters 3.3.3 Test methods

39 39 39 40 41 41 41 41

4. Results and discussion

4.1 Statistical findings 4.1.1 Observational error 4.1.2 Normality of test data 4.1.3 Repeatability parameters

4.1.4 Distribution of repeatability parameters 4.1.5 Influences on the repeatability parameters 4.1.6 Discussion on statistical findings

4.2 Modelling of rebound hardness

4.2.1 Existing proposals for prediction of compressive strength by rebound number

4.2.2 Graphical representation of R(t) - f

(t) data 4.2.3 Gaede’s model

4.2.4 Introduction of the phenomenological model 4.2.4.1 Composition of the model

4.2.4.2 Parametric simulation for the model 4.2.4.3 Experimental verification of model 4.2.5 Discussion on the phenomenological model 4.3 Targeted experimental results

4.3.1 Role of strength and stiffness in surface hardness 4.3.2 Role of water-cement ratio in time dependent behaviour 4.3.3 Discussion on targeted experimental results

43 44 50 53 55 60 63 64 64 67 68 69 70 72 75 77 78 78 80 82

5. Conclusion and future work

5.1 Hypotheses and new scientific results 5.1.1 On the statistical analysis 5.1.2 On the modelling

5.1.3 On the targeted experiments 5.2 Theoretical and practical benefits 5.3 Outlook and future work

85 85 88 90 91 92

List of publications i

Acknowledgements iii

References v

Appendices

Appendix A – Numerical input for the statistical analysis together with the resulted repeatability parameters

Appendix B – Results of the goodness of fit tests of the repeatability parameters

Appendix C – Results of the model verification experiments Appendix D – Results of the targeted experiments

A1-A170

B1-B128

C1-C18

D1-D2

Summary

The author of present thesis has devoted her research time to investigate the rebound hardness and its relationship to compressive strength from several aspects during the last decade. The result of the extensive literature survey and the statistical analysis of available in-situ and experimental test data, as well as the theoretical considerations and own laboratory research are all rendering a salutation to Ernst Schmidt after six decades he had invented the original rebound hammer.

The detailed statistical study was made on a large database of 60 years laboratory and in-situ experience, covered several thousands of test areas providing more than eighty thousand individual rebound index readings for analysis. It was demonstrated that several gaps are found in this field both in current technical literature and standardisation. The PhD study succeeded in providing general statistical characteristics for rebound surface hardness of concrete. Based on a comprehensive statistical analysis it was demonstrated that the within-test variation (repeatability) parameters of the rebound hardness method have similar tendency to that of the within-test variation parameters of concrete strength; i.e. no clear tendency is found in the standard deviation over the average and a clear decreasing tendency can be observed in the coefficient of variation by the increasing average. The probability distribution of the within-test standard deviation and the coefficient of variation of the rebound index, as well as of the rebound index ranges of individual test areas were not found to follow the normal distribution, but all the three parameters have a strong positive skewness.

Based on a comprehensive literature review it was realized that despite the numerous proposals neither general theory nor empirical function has been developed in the last 60 years that could describe the relationship between the measured surface hardness values and the compressive strength of concrete. Only one semi-empirical derivation for such a relationship was attempted by the designer of the original rebound hammer, but the model covered also the Brinell hardness of concrete. As a consequence, that model can not be generally used since very limited data have been published for the Brinell hardness of cementitious materials. Present PhD research has revealed the most pronounced influencing parameters for the rebound surface hardness of concrete and a phenomenological model was developed that can describe the time dependent behaviour of the rebound index vs. strength relationship and the unambiguous influence of the water-cement ratio. An extensive experimental verification of the model clearly demonstrated its reasonable application possibilities for different cements on a wide range of water-cement ratios and ages of concrete at testing. Based on a parametric simulation it was also realized that the model is robust and gives realistic formulation for the time dependent behaviour of the rebound surface hardness of concrete.

Results of targeted experiments demonstrated that the rebound index is a material property which is sensitive to the impact energy of the device and the strength and stiffness of concrete. It was found experimentally that the lower the impact energy of a dynamic hardness tester is, the more likely the hardness value can be related to the Young’s modulus, particularly in case of small water-cement ratios; and the higher the impact energy of the dynamic hardness tester is, the more likely the hardness value can be related to the compressive strength, particularly in case of high water-cement ratios.

Results of present research were welcome in the technical literature.

Notations

a shape parameter of probability distribution functions b shape parameter of probability distribution functions c scale parameter of probability distribution functions d location parameter of probability distribution functions f

compressive strength at the age of 28 days

f

characteristic compressive strength f

mean compressive strength of concrete

f

mean compressive strength of concrete tested on cube specimen of 150×150 mm f

mean compressive strength of concrete tested on cube specimen of 200×200 mm f

mean compressive strength of concrete at the age of 28 days

f

mean compressive strength of concrete at the age of 7 days

f

mean compressive strength of concrete tested on drilled core specimen f

mean compressive strength of concrete tested on cylinder specimen h

the height from an impacting ball is falling

h

rebound height of an impacting ball

k margin parameter (e.g. percentage point of the standardized range) L

initial length of the plunger

m[x] median value of a random variable n total number of rebound index readings

n

number of rebound index readings of even numbers n

number of test repetitions corresponding to in-situ test n

number of rebound index readings of odd numbers n

number of test repetitions corresponding to strength test

p acceptable error for the evaluation of average value of concrete strength r range

r

range of rebound index

s corrected sample standard deviation

s

within-test corrected sample standard deviation of rebound index

s

within-test corrected sample standard deviation of the even rebound index readings s

within-test corrected sample standard deviation of the odd rebound index readings t time, age of concrete

v

velocity reached by the impact body/hammer mass before impact v

[x] 95% percentile value of a random variable

w/c the ratio of the mass of water and the mass of cement in 1 m

compacted fresh concrete x

path driven by hammer mass before impact

x

path driven by hammer mass after impact

B beta function

C

coefficient of restitution D

domain of a function

E[x] mean value of a random variable

E

kinetic energy of the hammer mass just before the impact

E

Young’s modulus of concrete E

mean Young’s modulus of concrete

E

mean Young’s modulus of concrete at the age of 28 days E

mean Young’s modulus of concrete at the age of 7 days E

kinetic energy of the hammer mass right after the impact

HL Leeb hardness

Mo[x] mode (modus) value of a random variable N (  ,  ) normal probability distribution

P preset probability

Q notation of coefficient of restitution provided by the Silver Schmidt hammer R

rebound index at the age of 28 days

R

rebound index provided by L-type rebound hammer

R

rebound index of concrete provided by L-type rebound hammer at the age of 7 days R

mean rebound index

R

average of the even rebound index readings R

average of the odd rebound index readings

R

rebound index provided by N-type rebound hammer

R

rebound index of concrete provided by N-type rebound hammer at the age of 7 days V coefficient of variation

V

within-test coefficient of variation of the indirect measure V

coefficient of variation corresponding to in-situ test

v

velocity reached by the impact body/hammer mass after impact V

within-test coefficient of variation of rebound index

V

coefficient of variation corresponding to strength test W statistic of the Shapiro-Wilk normality test

 diameter of the tip of the Wolpert Leeb hardness tester α

multiplier for taking carbonation into account



skewness of a probability distribution of the standard deviation of rebound index γ

multiplier for taking strength development and type of cement into account



skewness of a probability distribution of the range of rebound index

 logarithm decrement



elastic deformation of concrete



local crushing (pseudo-plastic deformation) of concrete



elastic deformation of the plunger

 studentized range



studentized range of rebound index λ transformation parameter

 mean value

 degree of freedom

 real standard deviation



real variance

 phase shift

χ

chi-squared goodness of fit test

 standardized range

 gamma function

Δ  empirical additive parameter

Glossary

Accuracy: closeness of computations or estimates to the exact or true values that the statistics were intended to measure (OECD, 2008).

Batch-to-batch variation: reproducibility (ACI, 2003).

Bias: an effect which deprives a statistical result of representativeness by systematically distorting it, as distinct from a random error which may distort on any one occasion but balances out on the average (OECD, 2008).

Frequency: the number of occurrences of a given type of event or the number of observations falling into a specified class (ISO 3534-1).

GOF: goodness of fit test = statistical test for assessing whether a given distribution is suited to a data-set Kurtosis: a term used to describe the extent to which an unimodal frequency curve is “peaked”; that is to say, the extent of the relative steepness of ascent in the neighbourhood of the mode. The term was introduced by Karl Pearson in 1906 (OECD, 2008).

Modus: the Latin name for mode; the value that appears most often in a set of data (OECD, 2008).

Observational error: operator error in the use of original Schmidt rebound hammer due to the inaccurate reading of the index rider scale.

Performance error: operator error in the use of original Schmidt rebound hammer due to the inaccurate inclination of the device (i.e. not precisely perpendicular to the tested surface) during impact.

Phenomenological theory: a theory that expresses mathematically the results of observed phenomena without paying detailed attention to their fundamental significance (Thewlis, 1973).

Precision: the property of the set of measurements of being very reproducible or of an estimate of having small random error of estimation (OECD, 2008).

Random error: an error, that is to say, a deviation of an observed from a true value, which behaves like a variate in the sense that any particular value occurs as though chosen at random from a probability distribution of such errors (OECD, 2008).

Repeatability: precision under conditions where independent test results are obtained with the same method on identical test items in the same laboratory by the same operator using the same equipment within short intervals of time (ISO 3534-1).

Reproducibility: precision under conditions where test results are obtained with the same method on identical test items in different laboratories with operators using different equipment (ISO 3534-1).

Skewness: a term for asymmetry, in relation to a frequency distribution; a measure of that asymmetry (OECD, 2008).

Standardized range:  =r/  .

Studentized range:  =r/s, the difference between the largest and smallest data in a sample measured in units of sample standard deviations (Harter, 1960).

Within-test variation: repeatability (ACI, 2003).

CHAPTER 1 introduction

F irst chapter of present thesis introduces the scientific background of the research topic. The significance of hardness testing of materials is outlined as a non-destructive test method.

Based on a comprehensive literature review and own experiences the concerns and contradictions about the rebound surface hardness of concrete are highlighted. Objectives are defined in conformity with the findings introduced as research significance.

1.1 Scientific background

Concrete is a construction material that has the most widespread use in civil engineering and that is the manmade material produced in the largest quantity.

Compressive strength of concrete is the most important input data for engineering calculations during the design of reinforced concrete structures. Compressive strength of concrete can be determined by testing of moulded specimens or by core specimens drilled from existing structures.

In testing, the specimens are loaded up to failure to find compressive strength, usually under standardized laboratory testing conditions.

Moulded specimens, however, do not always represent the actual condition of structural concrete and drilling of core specimens from certain structural members is not always possible (because of risk of the loss of structural stability or bad accessibility of the structural element to be examined).

With non-destructive testing (NDT) devices the measurements can be performed directly on the structural concrete and the strength of concrete can be estimated from the measured results with limited reliability.

Several different non-destructive testing (NDT) methods were developed to estimate the strength of concrete in structures. The most successful strength estimation methods involve principles, which make the direct or indirect consequences of the compressive strength determining factors measurable or (in some cases) provide strength estimation by moderately destructive in-situ measurements.

One of these methods is the subject of present research: a classic NDT method based on the surface hardness testing of concrete which became popular in the construction industry during the 1950’s.

Surface hardness testing is a long established NDT method for the strength estimation of materials.

Hardness testing was the first material testing practice from the 1600’s in geology and engineering by the scratching hardness testing methods (Barba, 1640; Réaumur, 1722; Haüy, 1801; Mohs, 1812);

appearing much earlier than the systematic material testing that is considered to be started in 1857

when David Kirkaldy, Scottish engineer set up the first material testing laboratory in London, Southwark

(Timoshenko, 1951). The theoretical hardness research was initialized by the pioneering work of

Heinrich Hertz in the 1880’s (Hertz, 1881). Hertz’s proposal formed also the basis of the indentation hardness testing methods by Brinell, 1900; Rockwell, 1920; Vickers, 1924 and Knoop, 1934 (Fisher- Cripps, 2000).

Researchers adopted the Brinell method to cement mortar and concrete to find correlations between surface hardness and strength of concrete during the four decades following that Brinell introduced his ball indentation method for hardness testing of metals.

As further developments, dynamic surface hardness testing devices also appeared (Durometer by Albert F. Shore, 1920; Duroskop by Rational GmbH, 1930; spring hammer by Gaede, 1934; pendulum hammer by Einbeck, 1944).

In Switzerland Ernst Schmidt developed a spring impact hammer of which handling were found to be superior to its predecessors (Schmidt, 1950) and became very popular in the in-situ material testing due to the inexpensive testing device and its relatively simple use.

Nowadays, the Schmidt rebound hammer is still the surface hardness testing device of the most widespread use for concrete rather than devices of plastic indentation hardness testing. Rebound hammer can be used very easily and the measure of hardness (i.e. the rebound index) can be read directly on the display of the testing device.

In the rebound hammer (Fig. 1.1) a spring (1) accelerated mass (2) is sliding along a guide bar (3) and impacts one end (a) of a steel plunger (4) of which far end (b) is compressed against the concrete surface.

The impact energy is constant and independent of the operator, since the tensioning of the spring during operation is automatically released at a maximum position causing the hammer mass to impinge with the stored elastic energy of the tensioned spring. The hammer mass rebounds from the plunger and makes an index rider (5) moving before returning to zero position. Original Schmidt rebound hammers record the rebound index (R): the ratio of paths driven by the hammer mass during rebound and before impact.

(1) ( 2)

(3) ( 4)

( 5)

(a ) (b)

Fig. 1.1 Structure of the rebound hammer.

The dissipation of the impact energy by the local crushing of concrete under the tip of the plunger makes the device suitable for strength estimation.

The study of hardness is a research topic frequently appearing in the technical literature of physics and material science, nevertheless, the theory of contact mechanics still has several gaps. The topic sometimes induces even a philosophical question: Is hardness a material property at all?

It should be mentioned here that scientific consensus does not exist for the term ‘hardness’ even for the definition of the word (Fisher-Cripps, 2000).

Aim of rebound hammer tests is usually to find a relationship between surface hardness and compressive strength to be able to estimate the strength of concrete with an acceptable error.

The existence of only empirical relationships was already considered in the earliest publications

(Anderson et al, 1955; Kolek, 1958) and also recently (Bungey et al, 2006).

The uncertainty of the estimated compressive strength, therefore, depends both on the variability of the in-situ measurements and the uncertainty of the relationship between hardness and strength.

To find a reliable method for strength estimation one should study all the influencing factors that can have any effect on the hardness measurement, and also that can have any effect on the variability of the strength of the concrete structure examined. The estimation should be based on an extensive study with the number of test results high enough to provide an acceptable reliability level. The estimation should take care of the rules of mathematical statistics.

Numerous empirical relationships between compressive strength and surface hardness of concrete can be found in the technical literature, but usually based on very simple laboratory tests, i.e. mainly univariate regression curves are available. Only a few extensive studies can be found that consider multiple influencing parameters together with detailed parameter analysis.

The following future trends should be considered affecting surface hardness of concrete.

Rapid development of concrete technology can be realized in recent decades. New types of concretes became available for concrete construction in terms of High Strength Concrete (HSC), Fibre Reinforced Concrete (FRC), Reactive Powder Concrete (UHPC), Self Compacting Concrete (SCC) and Lightweight Concrete (LC). The strength development of concretes in the 20

century is schematically represented in Fig. 1.2a (after Bentur, 2002). Technical literature considering rebound hammer test on special concretes is very limited (e.g. Pascale et al., 2003; Nehme, 2004; Gyömbér, 2004; KTI, 2005).

Considerable development is expected in this field in the future.

Environmental impact on concrete structures also tends to be changed recently. For example, the rate of carbonation is expected to be increased due to the increasing CO

concentration of air in urban areas as a result of the accelerated increase of CO

emission worldwide. CO

concentration in the atmosphere is increasing by 0.5% per year on a global scale (Yoon et al, 2007). Development of CO

concentration in the atmospheric layer has been considerably increased in the last 50 years, as shown in Fig. 1.2b.

Carbonation of concrete results an increase in the surface hardness without any change in the compressive strength. In the future, extensive studies are needed in this field to be able to develop relationships for the rate of carbonation considering special concretes available recently.

0 50 100 150 200 250 300

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 1950’s 1970’s

1990’s 2000’s

w/c ratio, – compressive strength, N/mm²

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 300

250 200 150 100 50 0

360

340

320

300

280

260

CO2concentration, ppm

1750 1800 1850 1900 1950 2000 year

Fig. 1.2 a) Development of concrete strengths in the last 60 years (Bentur, 2002), shaded region indicates the validity of use for the original rebound hammer; b) Increase of CO

concentration in the atmosphere in the last 250

years (Yoon et al, 2007).

1.2 Research significance

Based on a comprehensive literature review it was realized that several publications are available in the technical literature concerning experimental results and analyses, however:

– The assessment of statistical parameters based on a considerable collection of rebound index data is missing from the technical literature. Even the current standards and recommendations contain statistical parameters that are obtained by datasets of limited size.

– For the rebound method neither a general theory nor a general empirical formula was developed that can describe the relationship between measured hardness values and compressive strength. Nevertheless, it is deemed in some technical papers that the behaviour is commonly understood.

– As a result of the diversity of the numerous empirical proposals that can be found in the technical literature some researchers even state that the method is suitable only for assessing the uniformity of strength of concrete.

– Rebound hardness can be related to compressive strength only if a sufficient amount of energy can dissipate in the concrete during the impact. The inventor of the original rebound hammer fitted the impact energy of the hammer to concrete compressive strengths available in the 1950’s. The concrete construction technology, however, nowadays uses concretes of higher compressive strengths.

– Due to the lack of scientific consensus the rebound hammer is continuously loosing its role to estimate compressive strength of concrete by itself. E.g. current International and European standards exclude the use of the rebound method for strength estimation on its own due to the limited reliability reported.

Testing of drilled cores together with the rebound method is suggested for an acceptable reliability.

Above findings highlighted the need of detailed theoretical and laboratory research.

1.3 Objectives

Present PhD research intended to investigate the reasons of the concerns about the strength estimation of concrete with the rebound method and provide a comprehensive analysis of the rebound method for a better understanding of the hardness of concrete and its relation to compressive strength.

Three general objectives were aimed to achieve within the framework of present PhD research:

1) Based on an extensive literature survey and statistical analysis of available in-situ and laboratory test data it was intended to ascertain whether the tendency and the distribution of variability parameters of rebound hardness are similar to that of the compressive strength. Precision statements of the available recommendations were intended to be monitored.

2) Based on an extensive literature survey and theoretical considerations the main governing parameters of the rebound hardness were intended to be identified considering exclusively properly prepared concretes.

After studying general laws related to the rebound index and compressive strength of concrete and detecting their interrelationships a phenomenological model was intended to be formulated. For the validation of the developed model parametric simulations, as well as laboratory verification tests were intended to be carried out.

3) Based on targeted laboratory experimental studies it was intended to demonstrate which mechanical

property can be related to the measured rebound hardness value by comparison of the development of

the tested properties with time and how the water-cement ratio of concrete and the impact energy of the

hardness tester device influence the rebound index.

CHAPTER 2 literature review

P resent chapter gives a historical overview on the development of hardness testing of materials. Rebound hardness tester devices and their operating principle – including the impact phenomena – are introduced. Influencing parameters of the rebound index are interpreted. Considerations about variability parameters of rebound hardness and minimum number of repetition of rebound index reading are presented. The main aim of the rebound hammer test is introduced and regression techniques are described for the relationship between the rebound index and compressive strength of concrete. As a closing subchapter an overview is given about the international and Hungarian standardization practice.

2.1 Historical overview

Hardness can be considered to be one of the oldest technical terms in languages, however, in common language the meaning of hardness, rigidity, stiffness, strength, toughness and durability are mixed up. In the earliest human written scripts these meanings were usually covered by the same term and only the context helped the reader to sense the real meaning. As several thousand years old examples, the Egyptian word ā ḥ ā- t (its hieroglyph is:  ) with the mixed meaning of stiff and hard or the Sumerian word nam-kalag-ga (its cuneiform script is: ) with the mixed meaning of hardness and strength can be mentioned here. The word isikku of Sumerian origin was used for the hardness of potter’s clay.

Technical literature (Walley, 2012) calls the attention to one of the earliest written references to hardness of materials with a similar meaning to that of today in the books of Hebrew prophets in the Bible (e.g. Ezekiel 3:9 “Like emery harder than flint have I made your forehead”; English Standard Version translation, 2001).

In-situ surface hardness testing of materials is a long established method for performance control,

mostly with the explicit or hidden aim of strength estimation. First appearance of the concept of

hardness testing in a written report goes back to 1640 when Alvaro Alonso Barba came with the

proposal of file scratch testing of minerals in one of his manuals prepared for the Spanish royal court on

ore mining and metallurgy (Barba, 1640). In 1690 Christian Huyghens published his study on light (Traité

de la lumière) in which the scratching resistance of Iceland Spar by knife cut was described at two

different angles to the sliding direction (Huyghens, 1690). In 1722 René Antoine Ferchault de Réaumur

published his study on metallurgy (L’Art de convertir le fer forgé en acier) in which scratching and special

contact hardness testing of metals were introduced (Réaumur, 1722). In 1729 Pieter van

Musschenbroek addressed a chapter to hardness testing in his thesis (Physicae Experimentales et

Geometricae Dissertations) in which a chisel instrumented pendulum hammer was introduced for the dynamic hardness testing of woods and metals (Musschenbroek, 1729).

The scratching hardness test was refined by Friedrich Mohs in 1812 in its present form of the 10- minerals scratching hardness scale used worldwide in mineralogy after several decades of development by others (Mohs, 1812). First proposal of a scratching hardness scale of different minerals can be credited to Wallerius (1747) and further ideas came from Kvist (1768), Werner (1774), Bergman (1780) and Haüy (1801) (Todhunter, 1893).

The conception of relative hardness based upon the power of one body to scratch another is evidently very unscientific. Huyghens had shown a century earlier that the hardness of a material varies with direction, and its power to scratch varies also with the nature of the edge and face (Todhunter, 1893).

The pioneering theoretical studies of Heinrich Hertz in the 1880’s on mathematical modelling of linear elastic contact has shifted the experimental hardness testing towards the indentation methods (Hertz, 1881). The first static indentation hardness testing laboratory device was developed by Johan August Brinell and was introduced to the public at the 1900 Paris Exposition Universelle (Brinell, 1901).

Hertz’s proposal formed also the basis of the later indentation hardness testing methods (Rockwell, (1920), Vickers (1924) and Knoop (1934) (Fischer-Cripps, 2000). These conventional methods involve in different ways the measurement of the size of a residual plastic deformation impression in the tested specimen as a function of the indenter load.

In-situ testing of concrete structures was started in the 1930’s. The testing methods at that time covered chisel blow tests, drilling tests, revolver or special design gun shooting tests, splitting tests, pull-out tests, strain measurements from loading tests (Skramtajew, 1938).

Researchers adopted the Brinell method to cement mortar and concrete to find correlations between surface hardness and strength of concrete in the four decades following that Brinell introduced his ball indentation method for hardness testing of steel (Crepps, Mills, 1923; Dutron, 1927; Vandone, 1933;

Sestini, 1934; Steinwede, 1937).

As a further development, dynamic surface hardness testing devices also appeared (Durometer by Albert F. Shore, 1920; Duroskop by Rational GmbH, 1930).

The first NDT device for in-place testing of the hardness of concrete was introduced in Germany in 1934 which also adopted the ball indentation hardness testing method, however, dynamic load was applied with a spring impact hammer (Gaede, 1934).

The operating principle of the spring impact hammers (known as Frank hammer and Zorn hammer) was similar to that of the later Schmidt hammers (Fig. 2.1): the impact was performed by a hammer mass that is accelerated by a tensioned spring. The impact energy was adjustable to 1250 Nmm and 5000 Nmm. The impact ball was exchangeable to different diameters. It was possible to reach with these parameters that the residual indentation diameter on the concrete surface became 0.3 to 0.7-times of the diameter of the impact ball. The strength assessment was based on empirical relationships between the indentation diameter and the compressive strength of concrete (Gaede, 1952).

Similar device was developed in the UK in by Williams, 1936. The hardness tester had the shape similar to a handgun with a mass of 0.9 kg and a tensioned spring provided the impact energy for an impact ball to test the hardness of concrete surfaces. The impact energy was reported to be relatively small:

the indentation depth of the ball in case of concretes of about 7 N/mm

was found to be about 1.5 mm.

The inventor suggested a strength estimation relationship based on 200 empirical data points.

The indentation testing technique was found to be the most popular in the European testing practice for

decades according to its relatively simple and fast operation (Gaede, 1934; Williams, 1936).

Fig. 2.1 Frank hammer and Williams hammer.

Later several other NDT instruments were introduced adopting the same method, e.g. pendulum hammer by Einbeck (1944) or different methods, e.g. pull-out testing and firearm bullet penetration testing by Skramtajew (1938); drilling method by Forslind (1944); ultrasound pulse velocity method by Long et al. (1945).

Fig. 2.2 indicates the sketch of the Einbeck pendulum hammer. Its operating principle is similar to the later Schmidt pendulum hammers. The device was suitable to test vertical concrete surfaces with a hammer of 2.26 kg of which head was ended in a ball indenter. The strength assessment was based on empirical relationships between the indentation diameter and the compressive strength of concrete. The Einbeck pendulum hammer was operated in full impact energy (run at 180° path) and half impact energy (run at 90° path) (Gaede, 1952).

Fig. 2.2 Einbeck pendulum hammer.

Further hardness testing devices can be also found in the technical literature. One of the most comprehensive surveys is found in the book of Skramtajew and Leshchinsky (1964) that is a good example for the outstanding innovation capacity of the former Soviet engineers: the book introduces more that 15 different surface hardness testing devices; most of them was Soviet development.

Nowadays the most widespread method for the surface hardness testing of concrete is the rebound hammer method that is appeared in the 1950’s by the Schmidt rebound hammer (also known as Swiss hammer) (Schmidt, 1950).

In Switzerland Ernst Schmidt developed a spring impact hammer of which handling were found to be

superior to the ball penetration tester devices (Schmidt, 1950). The hardness testing method of Shore

(1911) was adopted in the device developed by Schmidt, and the measure of surface hardness is the

rebound index rather than the ball penetration. With this development the hardness measurement became

much easier, as the rebound index can be read directly on the scale of the device and no measurements

on the concrete surface are needed (Schmidt, 1951).

The original idea and design of the device (Fig. 2.3) was further developed in 1952 (using one impact spring instead of two) resulted in simpler use (Fig. 2.4) (Greene, 1954; Anderson et al, 1955). Several hundred thousands of Schmidt rebound hammers are in use worldwide (Baumann, 2006). In 1954 Proceq SA was founded and has been producing the original Schmidt rebound hammers since then, without any significant change in the operation of the device (Fig. 2.5) (Proceq, 2005).

One of the latest developments of the device was finalized in November 2007, since the Silver Schmidt hammers (Fig. 2.6) are available (Proceq, 2008a). The digitally recording Silver Schmidt hammers can also measure coefficient of restitution, C

(or Leeb hardness; see Leeb, 1986) of concrete not only the original Schmidt rebound index. From 2011, the Silver Schmidt hammers are no more instrumented to record the original Schmidt rebound index, only the coefficient of restitution is measurable (referred as Q-value).

With this change the direct relationship between the two hardness values can not be studied, moreover the long-term experience with the original rebound hammer, thus the considerable amount of rebound index data can not be used anymore, that is a drawback from a scientific point of view.

Fig. 2.3 Original rebound hammer with two impact springs as of 1950.

Fig. 2.4 Original rebound hammer with one impact spring as of 1952.

Fig. 2.5 Original rebound hammer with one impact spring as of today.

Fig. 2.6 Silver Schmidt hammer.

The interested readers can find detailed information about further NDT methods for concrete in the technical literature (ACI, 1998; Balázs, Tóth, 1997; Borján, 1981; Bungey, Millard, Grantham, 2006;

Carino, 1994; Diem, 1985; Malhotra, 1976; Malhotra, Carino, 2004; Skramtajew, Leshchinsky, 1964).

2.2 Contact mechanical interpretation of hardness

The scientific definition of hardness has been of considerable interest from the very beginning of hardness testing, however, still today – more than 100 years after Hertz’s original proposal – no absolute definition of hardness is available in material sciences.

According to Hertz, hardness is the least value of pressure beneath a spherical indenter necessary to produce a permanent set at the centre of the area of contact. As Hertz’s criterion has some practical difficulties, the hardness values defined by the practical methods usually indicate different relationships between the indenter load and the tested specimen’s resistance to penetration or permanent deformation.

The intention to understand and explain hardness or determine a material property that can be estimated from hardness measurements sometimes induces even philosophical questions: Is hardness a material property at all? Does compressive strength exist?

If one accepts the practical conclusion that a hard material is one that is unyielding to the touch, it can be

evident that steel is harder than rubber (O’Neill, 1967). If, however, hardness is considered as the resistance

of a material against permanent deformation then a material such as rubber would appear to be ‘harder’ than

most of the metals: the range over which rubber can deform elastically is very much larger than that of

metals. If one focuses on hardness testing, it can be realized that properties influencing the elastic behaviour

play a very important part in the assessment of hardness for rubber-like materials, however, for metals the

deformation is predominantly outside the elastic range and involves mostly plastic properties (although the

elastic moduli are large, but the range over which metals deform elastically is relatively small).

Plastic deformation is normally associated with ductile materials (e.g. metals). Brittle materials (e.g.

concrete) generally exhibit elastic behaviour, and fracture occurs at high level of loads rather than plastic yielding. Pseudo-plastic deformation is observed in brittle materials beneath the point of an indenter, but it is a result of densification, where the material undergoes a phase change as a result of the high value of compressive stress in a restrained deformation field beneath the indenter.

The softening fashion of the pseudo-plastic material response with increasing volume of the material is considerably different from that can happen to metals during plastic deformation (where the volume of the material is unchanged during yielding) (Tabor, 1951). It can be realized during indentation hardness testing that the residual plastic deformation impression is a result of a three-dimensional, constrained deformation field that is strongly affected by the testing method itself (e.g. the indenter can be a sphere, cone, pyramid, diamond etc.). In case of ductile materials plastic deformation exists beneath the surface constrained by the surrounding elastically strained material. With further loading the plastic deformation extends to the surface of the specimen. The value of the mean contact pressure, which does not increase with increasing indenter load, is related to the hardness number. For hardness methods that employ the projected area, the hardness number is given directly by the mean pressure.

Cone cracks are forming at the contact surface in the case of elastic-brittle materials, however, plastic deformations can also be realized due to the local densification through phase change of the material as a result of high compressive stresses (this deformation is considerably different in nature from the plastic yield of ductile materials) (Fischer-Cripps, 2000).

Nevertheless, the theoretical approaches of contact mechanics and hence that of hardness has several gaps, the hardness (even in-situ) testing of materials offers the potential of strength estimation by means of a much simpler test than the direct compressive or tensile strength testing. This is the reason why several different hardness testers became available for material testing and the research on hardness of materials has been very dynamic from the beginning up to present day.

In some cases, particularly on dynamic hardness measurements, the elastic properties may be as important as the inelastic properties of the material.

Amongst several different indenter geometries the spherical indenters can be used for testing both ductile materials (e.g. metals) and brittle materials (e.g. ceramics). The response of materials to the indentation test includes elastic (reversible) and plastic (irreversible) deformations as well as forming of cone cracks in brittle materials; therefore, the definition of the term ‘hardness’ is not evident.

2.3. Types of rebound hammers

The concrete rebound hammers use the scleroscope method introduced by Shore in 1911 (Shore, 1911).

Scleroscope devices are impact testers in which spring accelerated or gravity accelerated hammer

masses impinge against the tested surface and the hardness index is defined as a measure of the impact

rebound. Two types of hardness index are defined usually: 1) the ratio of the paths driven by the hammer

mass after and before impact (R-value), and 2) the ratio of the velocities of the hammer mass after and

before impact (Q-value). Both types of hardness index are used for metal as well as for concrete hardness

testing (see Table 2.1).

Table 2.1 Scleroscope hardness testing methods.

Hardness index based on hammer mass rebound:

R-value

Hardness index based on hammer mass velocity:

Q-value or C

-value for concretes

The original design of Schmidt rebound hammer

The 2008 design of Silver Schmidt rebound hammer for metals

SKL scleroscope

Duroskop tester Leeb tester

2.3.1 Leeb hardness tester

The measurement mechanism of the Wolpert Leeb hardness tester is different from that of the concrete rebound hammers (Wolpert, 2006). A mass is accelerated by a spring toward the surface of a test object and impinges on it at a defined velocity, i.e. kinetic energy. The principle of the measurement is implemented by means of an impact body which has a spherical tungsten-carbide tip. The velocities before and after the impact are both measured in a non-contact mode by a small permanent magnet within the impact body which generates an induction voltage during its passage through a coil. The voltage recorded is proportional to the velocity of the impact body (Fig. 2.7). The Leeb Hardness, HL is defined as the multiple of the coefficient of restitution, Eq. (2.1):

v 1000 1000 v C HL

0

R  r 



Eq. (2.1)

In Eq. (2.1) v

indicates the velocity reached by the impact body before impact, while v

indicates the velocity reached by the impact body after impact, respectively.

The D-type impact device of the Wolpert Leeb hardness tester has much smaller weight (m = 5.5 g) compared to the hammer mass of the concrete rebound hammers as well as the tip of the device ( = 3 mm) provides much smaller contact area during impact, therefore, the within-test variation of the measured values may be increased by the effect inhomogeneity of the concrete surface tested. It can be also highlighted that the coefficient of restitution is a material property of which value strongly depends on the severity of the impact itself. The impact energy of the device is 11 Nmm.

before impact

after impact v0

velocity of the impact body

vr

time

1000 v HL v

0 r 



Fig. 2.7 The definition of Leeb Hardness, HL (Frank et al, 1986).

2.3.2 Rebound hammers

Concrete rebound hammers can be spring hammers or pendulum hammers. The original N-type rebound hammer is used for normal strength concrete. The suggested compressive strength range of the tested concretes is 10-70 N/mm

. The impact energy of the device is 2207 Nmm (Fig. 2.4, Fig. 2.7).

For completeness, the other types of rebound hammers are also listed here which are used for special cases, but these are not discussed in details within the scope of present thesis.

Fig. 2.8 N-, M- and P-type rebound hammers.

The NR-type rebound hammer can be used for the same purposes and in the same manner as the N-type rebound hammer, which records the rebound indices on paper. The DIGI-Schmidt hammer was also designed for normal strength concretes but it records the rebound indices digitally. The L-type rebound hammer was developed for testing of small or thin walled (<100 mm) concrete members or natural stone structural elements. The impact energy of the L-type device is one-third of the N-type device: 735 Nmm.

The LB-type hammer has the same impact energy as that of the L-type has and can be used for ceramic structural elements (e.g. brick). The only difference is the shape and size of the tip of the plunger of the device. The impact energy (29430 Nmm) and the size of the M-type rebound hammer are much higher but its structure is identical with the structure of the smaller devices. It was mainly designed for high strength concrete pavements (Fig. 2.8). A pendulum type (P-type) rebound hammer is also manufactured. It is suggested to be applied on surfaces of low strength construction materials (stones, ceramics, mortars, lightweight concretes and normal strength concretes at early age). Its impact energy is 883 Nmm, the tip of the pendulum is enlarged (Fig. 2.8).

Present PhD study focuses exclusively on spring hammers that are indicated as N-type or L-type rebound hammers by the original design of Ernst Schmidt.

Rebound hammers are devices that are calibrated by the operator therefore operators should have a

calibration anvil (EN 12504-2:2012). Before and after testing, but at least after every 1000 rebound it should

be checked whether the mechanical parts of the device are functioning as intended, i.e the device is suitable

for the test (the accepted rebound index by the N-type rebound hammer on the anvil is 81±2). If the rebound

hammer is used on a metal surface different from the calibration anvil the curved surface of the plunger can

be damaged, therefore it is not allowed (Proceq, 2004). Rebound hammers are allowed to be used only within

the temperature limits –10°C and +60°C according to the recommendations of the instruction manuals. The

EN 12504-2:2012 standard is stricter in this respect: the allowed temperature range is +10°C to +35°C.

2.4 Operating principle of the rebound hammer

In the rebound hammer (as can be studied in Fig. 1.1) a spring (1) accelerated mass (2) is sliding along a guide bar (3) and impacts one end of a steel plunger (4) of which far end is compressed against the concrete surface.

The impact energy is constant and independent from the operator, since the tensioning of the spring during operation is automatically released at a maximum position causing the hammer mass to impinge with the stored elastic energy of the tensioned spring. The hammer mass rebounds from the plunger and moves an index rider before returning to zero position. Original Schmidt rebound hammers record the rebound index (R): the ratio of paths driven by the hammer mass during rebound and before impact;

see Eq. (2.2). Silver Schmidt hammers can record also the square of the coefficient of restitution (referred as Q-value): the ratio of kinetic energies of the hammer mass right after and just before the impact (E

and E

, respectively); see Eq. (2.3).

In Eqs. (2.2) and (2.3) x

and v

indicate path driven and velocity reached by hammer mass before impact, while x

and v

indicate path driven and velocity reached by hammer mass after impact, respectively.

x 100 R x

0 r 



Eq. (2.2)

100 C v 100

100 v E

Q E

0 2 r 0

r     



Eq. (2.3)

The phases of the rebound hammer test can be seen in Fig. 2.9. When the hammer mass impinges on the plunger, a compression stress wave starts to propagate toward the concrete within the plunger. The plunger deforms elastically during the stress wave propagation.

When the compression stress wave reaches the fixed end of the plunger (i.e. the concrete), part of the energy is absorbed in the concrete and the rest of the stress wave is reflected back in the plunger. The reflected compression wave returns to the free end of the plunger and accelerates the hammer mass to rebound. The absorbed energy at the fixed end results both elastic and pseudo-plastic deformations (local crushing) of the concrete. When the acceleration of the plunger is brought to rest the elastic deformation of the concrete recovers, however, a residual set is formed in the concrete under the tip of the plunger.

For detailed theoretical analysis the stress wave attenuation behaviour and structural damping capacity of cementitious materials should be also studied. The relationship between rebound index and concrete strength depends on the damping capacity of concrete in the vicinity of the tip of the plunger of the rebound hammer. Damping capacity can be described by several parameters (damping ratio; damping coefficient; logarithm decrement; Q factor; decay constant etc.), but measurements are very sensitive to the heterogeneity of the concrete.

Swamy and Rigby (1971) have found the logarithm decrement of cement mortar and concrete to be

dependent on the water-cement ratio, aggregate content and moisture condition. However, limited data

are available in this field in the technical literature.

L0 L0 – s 

_s 

L0

_p 

L0

_s+ _c 

L0 – s 

c 

s+p 

L0 – s 

p 

s+c+p 

L0 – s 

c+ p 

1) 2) 3) 4) 5) 6) 7)

Fig. 2.9 Phases of the rebound hammer test,

1) Collision of the hammer mass to the plunger 2) Elastic deformation of the plunger 3) Elastic deformation of concrete 4) Local crushing of concrete 5) Release of elastic deformation of concrete 6) Release of elastic deformation of the plunger 7) Rebound of the hammer mass (Notations: L

– initial length of the plunger, 

– elastic deformation of the plunger, 

– elastic deformation of concrete, 

– local crushing (pseudo-plastic deformation) of

concrete).

Based on experiments with polymer bodies Calvit (1967) has demonstrated that a simple relationship can be derived between the rebound height (h

) of an impacting ball (falling from height h

) and the damping capacity of a homogeneous, isotropic, viscoelastic semi-infinite solid body. Assuming that the impact is a half cycle of a sinusoidal vibration then the ratio of the energy dissipated (E

) to the energy stored and recovered (E

) in the half a cycle is equal to π ·tan  , where  is the phase shift (Ferry, 1961).

The term π ·tanθ is equal to the logarithm decrement (), therefore (Kolek, 1970a):





 



 tan

h h h E E

r r 0 r

d

, from which:



 

1

1 h h

0

r

Eq. (2.4)

Of course, it is not possible to derive such a simplified relationship for concrete due to the inelastic deformations in the concrete and stress wave attenuation in the plunger and in the concrete. Damping capacity of concrete is not studied in present PhD research.

2.5 Impact phenomena during the rebound hammer test 2.5.1 Theoretical considerations

The technical literature gives detailed information about the impact of elastic solids and the stress wave propagation in elastic media (Timoshenko, Goodier, 1951; Kolsky, 1953; Goldsmith, 1960; Johnson, 1972; Graff, 1975; Zukas et al, 1982; Johnson, 1985). Present chapter gives a simplified overview of the impact analysis of the Schmidt rebound hammer test without the aim of providing a complete study.

Basics of the theory of elasticity as well as of stress wave propagation are considered to be known,

therefore, omitted to be detailed here. Selection of references is given above for further reading.

For the analysis of impact phenomena connected to the Schmidt rebound hammer test one can apply a simple model for the plunger and the hammer mass of the device as a longitudinal impact of a rigid mass on one end of a long, elastic, uniform bar perfectly fixed at its far end, as the most simple approximation (Fig. 2.10).

fixed end m

v

m

, , E, A, I, L

 (t) 

x

c·t

Fig. 2.10 Simplified model of the hammer mass and the plunger of the rebound hammer as a long elastic uniform bar perfectly fixed at its one end.

Let us consider that the moving hammer mass collides with the plunger (elastic bar with one fixed end) at its distal end. Let m

be the hammer mass (m

= 0.38 kg for the N-type original Schmidt hammer) and v

is the impact velocity of the hammer mass (v

= 2.4 m/s according to Granzer, 1970). The equation of motion can be written generally as:

x dx AE u t dx

A u

2 2

2



 





or

2 2 2 2

x c u t

u



 





where

 

E

c Eq. (2.5)

The velocity of wave propagation (c) should be distinguished from the velocity (v

) introduced to the material particles of the plunger in the compressed zone by the compressive force of the impact as well as from the velocity (v) of the material particles of the plunger gained by the impact at the distal end. The velocity of wave propagation (c) can be expressed from the equation of momentum and, therefore, the velocity (v) of the material particles of the plunger can be given as a function of the uniform compressive stress () acting on the distal end of the plunger during impact (Timoshenko, Goodier, 1951):



 

v E Eq. (2.6)

Considering the hammer mass to be absolutely rigid, the velocity of material particles at the distal end of the plunger at the instant of impact (t = 0) become v

and the initial compressive stress is:







v

E Eq. (2.7)

Due to the inherent resistance of the plunger the velocity of the hammer mass and, therefore, the pressure on the plunger will gradually decrease and a compression wave is formed with a decreasing compressive stress travelling along the length of the plunger (Fig. 2.10). The change in stress with time can be obtained from the equation of motion of the hammer mass:

) t ( dt A

m

dv    Eq. (2.8)

where m

is the hammer mass, v is the variable velocity of the hammer mass, A is the cross sectional area of the plunger and (t) is the variable compressive stress at the distal end of the plunger.

Integration and rearrangement results:

m1 E A t

e v

v









 and

E A t

e ) t

(













 Eq. (2.9)

These equations are valid as long as t < 2L/c. At t = 2L/c the compressive wave with the front stress of



returns to the distal end of the plunger which is in contact with the hammer mass still moving. The velocity of the hammer mass can not change suddenly, therefore, the stress wave is reflected back similarly to that at the fixed end and the compressive stress at the surface of contact suddenly increases by 2

. This sudden increase of stress occurs at the end of every interval of time T = 2L/c, therefore, separate expression of (t) for each intervals should be obtained. The general expression for any interval of nT < t < (n+1)T is given as (Timoshenko, Goodier, 1951):

) T t ( s ) t ( s ) t

( 







Eq. (2.10)

If  = m

/m

accounts for the ratio of the plunger and the hammer mass then the individual stress functions are formed as (Timoshenko, Goodier, 1951):

0 < t < T

t 2 0

0

e

s

 





 Eq. (2.11)

T < t < 2T 



 



 



 

  















 

 





T 1 t 4 1 e

s

s

2 t 0 0

1

Eq. (2.12)

2T < t < 3 T

 





 



 



 

  



 



 

  















 

 



 2

2 2 T 2 t 0 1

2

T

2 t T 8

2 t 8 1 e

s

s Eq. (2.13)

3T < t < 4 T

 





 



 



 

  



 



 

  



 



 

  















 

 



 3

3 2

3 2 T 2 t 0 2

3

T

3 t 3 32 T 3 t T 24

3 t 12 1 e

s

s Eq. (2.14)

The instant when (t) becomes equal to zero indicates the end of the impact and the separation of the plunger and the hammer mass. The duration of the impact increases when  decreases. Taking into account the hammer mass of m

= 0.38 kg and the plunger of m

= 0.099 kg one can obtain t = 106.74 μs for the time of impact in the case of the N-type original Schmidt hammer that is 2t/T = 5.79 based on T = 2L/c = 36.85 μs with the assumption of c = 5047.5 m/s for the plunger made of steel.

Fig. 2.11 indicates the normalized compressive stresses ((t)/

) at the distal end and at the fixed end

of the plunger based on the above simplifications.