Abstract. The design and application of high performance materials demands extensive knowledge of the materials damage behavior, which significantly depends on the meso- and mi- crostructural complexity. Numerical simulations of crackgrowth on multiple length scales are promising tools to understand the damage phenomena in complex materials. In polycrystalline materials it has been observed that the grain boundary decohesion is one important mechanism that leads to microcrack initiation. Following this observation the paper presents a polycrystal mesoscale model consisting of grains with orthotropic material behavior and cohesive inter- faces along grain boundaries, which is able to reproduce the crack initiation and propagation along grain boundaries in polycrystalline materials. With respect to the importance of the ge- ometry of the grain structure modeling an advanced Voronoi algorithm is proposed to generate realistic polycrystalline material structures based on measured grain size distribution. The polycrystal model is applied to investigate the crack initiation and propagation in statically loaded representative volume elements of aluminium on the mesoscale without the necessity of initial damage definition. Future research work is planned to include the mesoscale model into a multiscale model for the damage analysis in polycrystalline materials.
For PE-HD, slow crackgrowth (SCG) is of importance [4, 6, 7, 8] since it is considered to be the major failure mechanism in polyolefins and it is typically occurring suddenly and unexpectedly . SCG is commonly discussed in terms of a craze-crack mechanism and comprises the three stages (i) crack initiation, (ii) crack propagation and (iii) residual fracture (final failure). Crack initiation is considered to emerge from a local stress concentration within the polymer. The local stress concentration results from inhomogeneities, surface scratches, notches, defects or other imperfections in the material. After a crack is initiated, the typical craze-crack mechanism starts after micro-voids (microcracks) developed in the plastic deformation zone at the crack tip. They grow to larger voids while fibrils are formed from highly orientated inter-void polymer material (craze) [10, 11]. Further crackgrowth occurs when the fibrils in the craze-zone fail. Depending on stress level and rate of loading, failure occurs due to chain scission, disentanglement or cavitation. For SCG, disentanglements are regarded as the dominant mechanism. Such failure results in fracture surfaces representing a macroscopic brittle behavior [5, 11, 12]. A major characteristic of the craze- crack mechanism is the significant generation of additional (internal) surface during crazing accompanied by a volume increase due to the formation of voids and fibrils . Therefore, this process is influenced by the environment. External fluids are able to change the surface energy and Van der Waals forces between polymer chains. Thus, the energy required for the generation of additional surface can be reduced. In contrast, a volume-constant ductile SD does not create additional surface. Due to the influence of fluids, the damage process occurring to PE-HD is also commonly termed environmental stress cracking (ESC). Usually, ESC is supposed to result when environmental fluids significantly influence the course of damage to PE-HD, e.g. the time to failure t f .
a continuous decrease in S-N curve was realized up to 10 10 cycles (Betzwar Kotas et al. 2013). These most recent
findings once again validate that a real fatigue limit (strength) does not exist for the hardmetals and the failure mechanism is mainly microstructure controlled.
The Paris relationship is frequently addressed by researchers and is important for evaluating the fatigue resistance of a component. Similarly beginning from the early work of Roebuck and Almond (1988) and later followed by others (Torres et al. 2001, Llanes et al. 2002, Hiroko et al. 2014) and similar to the Wöhler diagrams, an ideal fatigue crackgrowth (FCG) is not observed for the industrial grades. Generally, there is a scatter of the experimental data, which can be idealized under a linear trend. Hence, the FCG rate diagrams for the hardmetals are composed of linearized curve fits and it is almost impossible to distinguish between different stages of crackgrowth (Fig. 1b). Based on these results, it can be easily argued that, following the initiation phase the crack propagation in the hardmetals develops rapidly under increasing velocity followed by the instantaneous failure. Based on their study, Fry and Garret (1988) also report that, time dependent crackgrowth does not occur in hardmetals during fatigue, since crack velocity (�����) is also independent of the frequency of the loading.
Abstract We introduce trimmed likelihood estimators for processes given by a stochastic differential equation for which a transition density is known or can be approximated and present an algorithm to calculate them. To measure the fit of the observations to a given stochastic process, two performance measures based on the trimmed likelihood estimator are proposed. The approach is applied to crackgrowth data which are obtained from a series of photos by backtracking large cracks which were detected in the last photo. Such crackgrowth data are contaminated by several outliers caused by errors in the automatic image analysis. We show that trimming 20% of the data of a growth curve leads to good results when 100 obtained crackgrowth curves are fitted with the Ornstein- Uhlenbeck process and the Cox-Ingersoll-Ross processes while the fit of the Geometric Brownian Motion is significantly worse. The method is sensitive in the sense that crack curves obtained under different stress conditions provide significantly different parameter estimates.
Abstract. Various theories in the past have addressed the correlation of material properties and the respective acoustic emission release during fracture. Whilst these theories yield good predictions for fundamental relationships, they neglect the dynamic displacements during crack formation. This paper presents first results for a new acoustic emission crack source model based on a finite element modelling approach which calculates the dynamic displacement field during crack formation. The specimen modelled is statically loaded until conditions for crackgrowth (e.g. local exceedance of material’s fracture toughness) are fulfilled. Crackgrowth is modelled by local degradation of the material properties in the crack process zone. The respective displacements generate the acoustic emission signal and allow detailed examination of the generation of acoustic emission signals. Subsequent to crackgrowth signal propagation in a simple tensile specimen is modeled. The signal propagation is modeled superimposed to the static displacement field. The influence of the crack propagation length, the static displacement field and material plasticity is investigated. It is demonstrated, that present analytical theories systematically underestimate the strength of acoustic emission sources. Strong discrepancy was found between the rise-times predicted by the present simulations and those assumed in analytical theories.
The strains on the surface of a cracked specimen, resulting from a mechanical load- ing, cause deformations at the firmly adhered piezoelectric PVDF film. Thus, on its surface, charges and electric potentials, respectively, are generated which are mea- sured at discrete locations using an array of electrodes. The aim of the presented sensor concept is to identify the crack position and the fracture mechanical quanti- ties from these potential values. Concerning mechanical properties, the polymeric PVDF material has significant advantages compared to piezoelectric ceramics. The sensor concept is particularly suitable for monitoring cracks in plate and shell struc- tures under conditions of linear elastic fracture mechanics. Here, especially fatigue crackgrowth plays an important role, where the crack paths usually exhibit large radii of curvature and the mode I crack opening
To encounter the higher crackgrowth resistance of modern PE and PP pipe grades, the cracked round bar (CRB) specimen was introduced. Due to the possibility of asymmetric crackgrowth, three clip-on gauges positioned around the specimen perimeter were used in a variety of publications to gain crackgrowth data (Lang et al., 2005; Haager, 2006; Pinter et al., 2007; Pinter, 2007; Frank et al., 2008a; Frank et al., 2008b, Frank et al., 2009a, Frank et al., 2009b). New PP grades with even higher fracture toughness again surpass testing times of previous generations, but testing at elevated temperatures was found to allow for significantly reduced testing times (Arbeiter et al. 2014). However, to produce reliable crackgrowth data from tests with clip-on gauges at elevated temperatures proves to be impossible, since the clamping of the clip-on gauges fails and softening of the material surface introduces measurement errors. To overcome the limitations of contact-based measurements, optical systems enabling crackgrowth measurements from multiple perspectives offer great potential. While several ap- proaches are conceivable, up to now only optical measurements of CRB crackgrowth via two cameras to compensate the asymmetric crackgrowth were already conducted in former stud- ies (Schöffl, 2014; Saberi Fathi, 2014), but temperature test chamber designs usually limit the observer to a single point of view.
23 stress intensity factor Kth is of high significance. This threshold stress is not only a material characteristic, but also depends on the maximum tensile stress (KI,max) and the R-ratio (KI,min/KI,max) respectively. It specifies a certain threshold stress intensity factor Kth, below which the crack does not propagate (Lang, 2013). The most relevant factors to describe crackgrowth under cyclic loading are the crackgrowth rate (da/dN), where da represents the infinitesimal ingress of the crack size per increasing number of load cycle (dN) and the stress intensity factor range for cycling loading ∆KI as well as the R-ratio of the loading profile. Equation 2.5 can now be expressed for a time dependent loading profile and a Mode I loading situation, with 𝜎(𝑡) being the time dependent applied stress and a being the current crack length:
A suitable device was designed and built for the observation of the crackgrowth resistance (“R- curves”). The aim was to have a test device that is small enough to fit into a conventional microscope and that is as rigid as possible to enable stable crackgrowth even for rather brittle ceramics like the yttria coatings. A massive frame was chosen to achieve a minimum deformation under load. A brief stress FE-analysis showed that the deformation for the maximum expected loads of 100 N is less than half a micron for the load frame in the vicinity of the outer load bearing rollers. The inner rollers are positioned on a crowned support to compensate for minor deviations from the parallelism of the sample surfaces. The load is applied by means of a stiff piezo stack (PI Instrumente, Germany) that has either a maximum force of 3 kN or a maximum travel of 60 µm. Since the displacement of the actuator is limited, a preload spindle is integrated into the load frame. The load cell (500 N, HBM, Darmstadt, Germany) is positioned between the piezo actuator and the support for the inner rollers. Figure 3 shows the piezo bending device. The crack propagation was observed by means of a light
More considerations went into the choice for the geometry for the crack propagation exper- iments. The fracture mechanical modelling imposed many of the requirements. The crack had to go through the entire thickness of the specimen and have a simple crack front. Furthermore, electrical fringing fields and the electric field singularity should be as small as possible leading to thin specimens (b À t). As crackgrowth is to be studied, a controlled starter crack should be introduced into the specimen and so the electrode was placed at the specimen edge. The stress in the electrode area introduced by the incompatible strains should be maximized which is achieved by choosing long specimens compared to the electrode width (L À b). By this choice stress relieve due to bending of the outer edges are confined to a comparably small area far away from the crack (see also figure 4.5). Finally, the clamping and the stresses should be as homogeneous as possible and so the electrodes should be narrow compared to the specimen length (W À b). A compromise of those requirements and the needs to ensure safe specimen handling led to plates of 40 × 40 mm 2 size and a thickness of 0.5 mm with a variation of the polarization state and the electrode coverage as seen in fig 1.13b. This configuration is called asymmetric as the electrode is not centered.
2 ( 2.4)
with B as the specimen thickness. After a certain amount of crack extension determined by a predefined increase in the voltage monitored ∆ K and accordingly ∆ F and are re- duced in steps whereas the initial reduction is the largest, as the crackgrowth rate is signifi- cantly high. With decreasing crackgrowth rate, the increment is decreased as well to prevent a crack stop by the preceding plastic zone. In each step a predefined increase in the voltage and thus a crack extension of approximately the same amount is bided. This stepwise reduc- tion of crack loading is continued until the crack is stopped. Under the last cyclic load after a million load cycles, no crack change should be measured. Only then is the test completed. In the meantime, the recorded potential data are stored in an Excel table with the load and test parameters being indicated.
Whether this method is suitable for a given matrix material depends on a few factors like, for example, the strength of the material. Because the driving force for crackgrowth, namely, the stress intensity factor or the J- integral, are not only dependent on the applied load but also the crack length, higher loads are necessary in the micro specimens compared with macroscopic specimens to reach the same driving force. If the material requires too much driving force to initiate and grow these fatigue cracks while simultaneously having a low strength, the challenge lies in being able to apply enough driving force without plastically deforming the specimen beforehand. This technique is therefore less applicable to pure metals, whereas materials that exhibit hardening on a length scale smaller than the obstacle of interest (e.g., solid- solution hardening or nanoscale precipitates) are suitable candidates for this technique.
Solar energy has become one of the major renewable energy sources that aim to bridge the gap between the energy demand and supply by offering more sustainable solutions (Buker et al., 2015). The global solar-thermal market has grown significantly over the last decade. This growth is more evident in more industrialized regions, such as Europe, the United States, and China with currently over 70 million households equipped with a solar hot water supply (Koehl et al., 2012). A solar-thermal collector is a device that converts the solar irradiation into a useful heat energy and conveys it through a transport fluid, such as air or water. In order to reach the highest possible efficiency, the absorber must be able to absorb as much solar irradiation as possible. Furthermore, it should transfer the generated thermal energy to the fluid medium with very low losses to the surrounding (Koehl et al., 2012). Solar-thermal collectors can be used for different purposes and over a wide range of applications, such as water heating, space heating and cooling, solar-thermal power systems and industrial process heat (Kalogirou, 2004). However, in this thesis, I will focus on polymers that are used for solar collectors of domestic hot water systems (DHW).
When a grown crack has been unloaded and is again loaded, the crack tip will only see loading by a stress intensity factor if K appl >K sh . Consequently, the shielding stress intensity factor causes a threshold value for the subcritical crackgrowth as is schema- tically illustrated in Fig 8b. The stress intensity at which K total and crackgrowth rate disappear in a crack-growth test under monotonously decreasing loading may be denoted as K appl (K tip =0)=K 0 . Then it holds for a crack-arrest test under decreasing load
This paper is targeted on numerical methods for accurate crack tip loading analysis and crack path prediction. Those are based on ﬁnite element calculations of the boundary value problem. Applying path-independent integrals to curved cracks in order to accurately calculate the J-integral, energy release rate (ERR) or stress intensity factors (SIF) is still not state of the art. Contours which are not conﬁned to the crack tip require special analytical preparation and numerical treatment to supply results which are su ﬃciently precise for reliable crack path prediction. Methods to improve the calculation of the J-integral and the interaction inte- gral (I-integral) are presented. In particular, the latter has never been applied to strongly curved cracks. Also, e ﬃcient methods for the loading analysis and crackgrowth simulation of multiple interacting cracks based on path-independent integrals are presented. The anisotropy of fracture toughness is taken into account being a crucial part of the numerical model. Experiments are carried out with specimens made of aluminum alloy Al-7075, comparing subcritically grown cracks with simulations.
Cracking in concrete is characterized by coalescence of microcracks, which finally join to a macroscopic discrete crack. This phenomenon can be modeled using the cohesive zone ap- proach, where stresses can be transferred through the interface accounting for the process zone. An important point for automatic crackgrowth simulations is the criteria, that determines the orientation and position of a new a crack, and how the crack propagation direction is deter- mined. In this paper different methods are compared to verify the applicability of each method. 2 EXTENDED FINITE ELEMENT METHOD
tear ridges, ductile dimples and transgranular fracture (1), which are typical for regime C FCG. 10 Furthermore, Figure 9B reveals broken primary intermetallic particles found throughout the fracture surface (2). Thus, the high-load FCG shows evidence of cyclic ductile stable rupture rather than fatigue striations, which should be predominant in regime B (Paris regime) crack propaga- tion. The scanning electron microscope (SEM) micro- graph in Figure 9C reveals that there was a relative movement of the S-mode fracture surfaces against each other, that means flattened areas (3) indicate physical contact of the fracture surfaces during crack propagation. Figure 9D shows scratches (marked as (4)) perpendicular to the crackgrowth direction (black arrow). The concept for the mode I crack closure in the classical sense indi- cates that forces are transmitted perpendicular to the fracture surfaces when they are in contact. 39 This is still possible in the V mode because of the interlocking of the fracture surfaces. In contrast, the surface contact for the S mode is more complex, as in-plane relative movements are possible in the 45 direction. Therefore, sliding of the 45 fracture surfaces against each other could locally cause additional mode II (in-plane shear) and mode III (out-of-plane shear) loads at the crack front, thereby lead- ing to very complex stress states that can increase crack propagation rates. The simulation model can only
We could also explore the nonequilibrium regime for all models by coupling the surface diffusion process to elastic fields, which can then provide an external driving force. Ex- posing an elliptical pore to external elastic loading lead to the expected slit-like form of the inclusion (Fig. 4.14), indicating that crackgrowth due to surface diffusion is possi- ble. For a quantitative analysis, we chose the Grinfeld instability as a highly nontrivial setup. The Grinfeld instability constitutes the link between pattern formation processes and conventional fracture mechanics; additionally, it is one of the rare cases where an- alytic results are available for comparison. All models could reproduce the spectrum of the instability very well, with the SM model again clearly showing the least quantitative agreement to the analytic expectation (Fig. 4.18). The first of our newly developed mod- els, the LCT model, is most efficient in suppressing the unwanted diffusion perpendicular to the interface. This analytically desirable property makes the model numerically less robust for situations where curvatures are small or the diffusion along the interface is not sufficiently fast. Our second new model, the GCT model, relaxes the strict requirement of local matter conservation, enforcing it only on a global scale. It proves to be extremely accurate, versatile and able to deal with variations of the interface width very well, mak- ing it the simulation method of choice in most cases.
In case of the polypropylene, a maleic anhydride acid crafted polypropylene (MAPP) is often used as coupling agent, which has a PP backbone and functional side groups. The functional principle of the coupling agent is shown in Fig. 4. It can be seen that MAPP owns nonpolar sections and polar functional side groups which react with the hydroxyl groups of the cellulosic fibers by building covalent ester bonds. The newly created carboxyl groups (‑COOH) can build hydrogen bonds with the free hydroxyl groups of the cellulosic fibers whereas the nonpolar backbone of the MAPP shows a high affinity the PP matrix. Applying this coupling agent provides an embrittlement of the composite CT-specimens and thus leads to much smaller plastic zones during crackgrowth.