Growing Crack Tip Research Articles

Statistical and reliability analysis for mixed-mode fracture tests applied to wood material

The integrity of timber structures is mainly related to its capacity to resist crack propagation under various load conditions. However, this phenomenon is random by nature, and the need to incorporate statistical information is mandatory for practical use in structures. This paper aims at defining a probabilistic model in order to characterize the scatter of the toughness test results of timber. The instantaneous failure tests are performed using the mixed-mode crack growth specimen. The crack tip growth is recorded by a video camera for mixed-mode ratios of 15°, 30° and 60°, where the relative displacement of loading points is recorded by LVDT sensor. The experimental energy release rate is evaluated by the compliance method. As large scatter of the energy release rate is observed, the statistical analysis is performed by using the bootstrap simulation, in order to characterize the probabilistic models in the opening and shear crack modes. The reliability analysis is then performed in order to underline the impact of the statistical uncertainties on the rupture of wood material.

A strong discontinuity based adaptive refinement approach for the modeling of crack branching

AbstractIn the current work, the physical phenomena of dynamic fracture of brittle materials involving crack growth, acceleration and consequent branching is simulated. The numerical modeling is based on the approach where the failure in the form of cracks or shear bands is modeled by a jump in the displacement field, the so called ‘strong discontinuity’. The finite element method is employed with this strong discontinuity approach where each finite element is capable of developing a strong discontinuity locally embedded into it. The focus in this work is on branching phenomena which is modeled by an adaptive refinement method by solving a new sub‐boundary value problem represented by a finite element at the growing crack tip. The sub‐boundary value problem is subjected to a certain kinematic constraint on the boundary in the form of a linear deformation constraint. An accurate resolution of the state of material at the branching crack tip is achieved which results in realistic dynamic fracture simulations. A comparison of resulting numerical simulations is provided with the experiment of dynamic fracture from the literature. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The effect of a single tensile overload on stress corrosion cracking growth of stainless steel in a light water reactor environment

It has been found that a single tensile overload applied during constant load amplitude might cause crack growth rate retardation in various crack propagating experiments which include fatigue test and stress corrosion cracking (SCC) test. To understand the affecting mechanism of a single tensile overload on SCC growth rate of stainless steel or nickel base alloy in light water reactor environment, based on elastic-plastic finite element method (EPFEM), the residual plastic strain in both tips of stationary and growing crack of contoured double cantilever beam (CDCB) specimen was simulated and analyzed in this study. The results of this investigation demonstrate that a residual plastic strain in the region immediately ahead of the crack tips will be produced when a single tensile overload is applied, and the residual plastic strain will decrease the plastic strain rate level in the growing crack tip, which will causes crack growth rate retardation in the tip of SCC.

Wedge indentation into elastic–plastic single crystals, 1: Asymptotic fields for nearly-flat wedge

Asymptotic stress and deformation fields under the contact point singularities of a nearly-flat wedge indenter and of a flat punch are derived for elastic ideally-plastic single crystals with three effective in-plane slip systems that admit a plane strain deformation state. Face-centered cubic (FCC), body-centered cubic (BCC), and hexagonal-close packed (HCP) crystals are considered. The asymptotic fields for the flat punch are analogous to those at the tip of a stationary crack, so a potential solution is that the deformation field consists entirely of angular constant stress plastic sectors separated by rays of plastic deformation across which stresses change discontinuously. The asymptotic fields for a nearly-flat wedge indenter are analogous to those of a quasistatically growing crack tip fields in that stress discontinuities can not exist across sector boundaries. Hence, the asymptotic fields under the contact point singularities of a nearly-flat wedge indenter are significantly different than those under a flat punch. A family of solutions is derived that consists entirely of elastically deforming angular sectors separated by rays of plastic deformation across which the stress state is continuous. Such a solution can be found for FCC and BCC crystals, but it is shown that the asymptotic fields for HCP crystals must include at least one angular constant stress plastic sector. The structure of such fields is important because they play a significant role in the establishment of the overall fields under a wedge indenter in a single crystal. Numerical simulations—discussed in detail in a companion paper—of the stress and deformation fields under the contact point singularity of a wedge indenter for a FCC crystal possess the salient features of the analytical solution.

Effect of welded mechanical heterogeneity on local stress and strain ahead of stationary and growing crack tips

The crack tip stress and strain condition is one of main factors affecting environmentally assisted cracking (EAC) behaviors in light water reactor (LWR). The mechanical and material properties of the base metal, weld metal and heat-affected zone (HAZ) in welded joints are heterogeneous because of the inherent characteristics of welded joint. Since the welded joint is more susceptible to EAC, to understand the effect of the strength mismatch in the welded joint on EAC growth rate, the stress and strain state in both stationary and growing crack tips of the welded joint specimen are investigated by the elastic–plastic finite element method (EPFEM) in this paper. The results indicate that the strength mismatch and sampling position in the welded joint would observably affect the stress and strain ahead of the stationary and growing crack tip, and accordingly affect the EAC growth rate.

Dynamic Growing Crack Tip Field in Visco-Elastic Compressible Material

A mechanical model of the visco-elastic compressible material is established in order to investigate the viscous effect in dynamic growing crack-tip field. The constitutive equations on the visco-elastic compressible material are deducted. Through asymptotic analysis, it is shown that in the stable creep growing stage, the elastic-deformation and the visco-deformation are equally dominant in the near-tip field, as 1 ( 1) n r− − . The asymptotic solutions of separative variable in the crack-tip field are aslo obtained. According to numerical calculation, the curves of stress, stain and displacement are given. The results indicate that the near-tip fields are mainly governed by the creep exponent n and Mach number M ; the stress fields of mode I and mode II is slightly affected by the elastic compressible deformation; the strain and displacement fields of mode I are deeply affected by the elastic compressible deformation. However, the strain and displacement fields of mode II are less affected by the elastic compressible deformation. The asymptotic solutions of dynamic growing crack-tip field gained here can conveniently degenerate the incompressible case, when the Poisson ratio 0.5 ν→ , named as HR field. The conclusions can provide the references for further studying the dynamic growing crack-tip field in compressible material.

Stress Field Evaluation for a Propagating Crack in a Thin Glass Plate

An instantaneous phase-stepping technique using a CCD camera equipped with a pixelated micro-retarder array is applied to the study of quasi-static crack growth in a quenched thin glass plate. The distributions of the principal direction as well as the principal stress diference around a growing crack tip are obtained by instantaneous phase-stepping photoelasticity. Then, not only the mixed-mode stress intensity factors but also the T-stress are evaluated from the distribution of the principal stress difference, and they are validated using the reconstructed phase maps. By applying the proposed method to the sucsessive images, the time-variations of the fracture mechanics parameters are evaluated quantitatively. Results show that the proposed instantaneous phase-stepping technique is effective for the study of the crack growth behavior in a thin glass plate

Toughening due to domain switching in single crystal ferroelectric materials

In this paper Mode I steady state crack growth in single crystal ferroelectric materials is investigated. Specifically, the fracture toughness enhancement due to domain switching near a steadily growing crack tip is analyzed. For this purpose, an incremental phenomenological constitutive law for single crystal ferroelectric materials is implemented within a finite element model to calculate the stress and remanent strain fields around the crack tip. Also, the ratio of the far field applied energy release rate to the crack tip energy release rate, i.e. the toughening, is calculated. The numerical computations are carried out for single crystal ferroelectric materials of tetragonal or rhombohedral structure with different switching hardening and irreversible remanent strain levels. Toughening levels for crack growth along different crystallographic directions and planes are obtained and compared. Results from numerical computations for the toughening anisotropy for both tetragonal and rhombohedral crystals are presented and discussed.

Instantaneous phase-stepping photoelasticity for the study of crack growth behaviour in a quenched thin glass plate

A new approach to simultaneous acquisition of phase-stepped photoelastic fringes using a CCD camera equipped with a pixelated micro-retarder array is described for the investigation of time-variant problems. This method is applied to the study of quasi-static crack growth in a quenched thin glass plate. The distributions of the principal direction as well as the principal stress difference around a growing crack tip are obtained by the proposed method. Then, not only the mixed-mode stress intensity factors but also the T-stress are evaluated from the distribution of the principal stress difference, and they are validated using the reconstructed phase maps. The results show that the proposed instantaneous phase-stepping technique is effective for the study of the crack growth behaviour in a thin glass plate.

Mechanical design after nature

The configurational force concept enables the derivation of the incremental plasticity J-integral Jep, which is, in contrast to the conventional J-integral, physically appropriate to characterize the crack driving force in cyclically loaded elastic–plastic materials with growing cracks. In this paper we apply Jep, combined with an analysis of the configurational force distribution, for the investigation of fatigue crack growth retardation after a single tensile overload. The motivation for this investigation is that the main reason for the overload effect, i.e. crack flank contact behind or residual stresses around the growing crack tip, is today still an open question in fatigue. Numerical case studies are performed for two-dimensional Compact Tension specimens with long cracks that grow under cyclic Mode I loading and plane strain conditions. Variables of the numerical case studies are the overload ratio and the load ratio during constant cyclic loading. The influence of crack flank contact is examined by a comparison of two different simulations: The first simulation assumes frictionless contact between the upper and lower crack flank; in the second, fictive case, it is assumed that crack flank overlap is possible. The results show that all features of the overload effect even occur, if crack flank contact is not possible. Finally, the ability of the effective stress intensity range ΔKeff to characterize the overload effect is also discussed.

Experimental determination of cohesive failure properties of a photodegradable copolymer

In this paper we present a methodology to measure the material traction-separation relation for a poly(ethylene carbon monoxide) copolymer, ECO. This material exhibits a ductile-to-brittle transition when subjected to ultraviolet irradiation and undergoes a change of failure mechanism, from shear yielding to crazing, in the process. Single edge notched tension specimens of ECO irradiated for 50 h were used to generate slow-speed stable crack growth, predominantly from material crazing. Full-field measurements of the in-plane deformation around the growing crack tip were performed using the optical technique of digital image correlation. A multicamera setup was used in which simultaneous measurement of both the far-field displacement and that directly surrounding the craze was performed. The far-field results were used to obtain a value of the energy release rate supplied to the crack tip region. The near-tip results were used to extract a material traction-separation law in the regime of steady-state crack growth. A softening traction-separation relation was measured. The area under the traction-separation curve was then compared with the simultaneous far-field measurements and the agreement was very good (within 6.5%) validating the experimental methodology used.

Development of a fundamental crack tip strain rate equation and its application to quantitative prediction of stress corrosion cracking of stainless steels in high temperature oxygenated water

A formulation for the quantitative calculation of the stress corrosion cracking (SCC) growth rate was proposed based on a fundamental-based crack tip strain rate (CTSR) equation that was derived from the time-based mathematical derivation of a continuum mechanics equation. The CTSR equation includes an uncertain parameter r 0, the characteristic distance away from a growing crack tip, at which a representative strain rate should be defined. In this research, slow strain rate tensile tests on sensitized 304L stainless steel in oxygenated high temperature water were performed. By curve fitting the experimental results to the numerically calculated crack growth rate, the parameter r 0 was determined. Then, the theoretical formulation was used to predict the SCC growth rates. The results indicate that r 0 is on the order of several micrometers, and that the application of the theoretical equation in predicting the crack growth rate provides satisfactory agreement with the available data.

The flow theory of mechanism-based strain gradient plasticity

The flow theory of mechanism-based strain gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to strain gradient effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734; Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3 (1996) 169].

Constraint effects on the elastic–plastic fracture behaviour in strain gradient solids

ABSTRACT Crack‐tip constraint effects (or T‐stress effects) on the elastic–plastic fracture behaviour in strain gradient materials are analysed in the present study. The T‐stress effects on the stress distributions along the plane ahead of the stationary and growing crack tip, respectively, are analysed by using the Fleck and Hutchinson strain gradient plasticity formation. For a steadily growing crack, the T‐stress effects on the steady‐state fracture toughness are analysed by adopting the embedded fracture process zone model. In addition, the analysis for the growing crack is applied to an interfacial cracking experiment for a metal/ceramic system, and the material length‐scale parameter appearing in the strain gradient plasticity theory is predicted. In the present analyses, a new finite element method specially designed for strain gradient problems by Wei and Hutchinson is adopted.

Simulation of JR-curves for reactor pressure vessels steels on the basis of a ductile fracture model

A procedure for the prediction of J R-curves for reactor pressure vessels (RPVs) steels in the initial and embrittled states is presented. Prediction of the J R-curves is performed over the ductile fracture temperature range on the basis of a ductile fracture model. A procedure for the determination of ductile fracture model parameters based on tests of smooth and notched cylindrical specimens is proposed. The stress and strain fields near the stationary and growing crack tip are analyzed by FEM. Approximate analytical solutions for stress and strain fields near a growing crack tip are proposed. Comparison of the predicted J R-curves and experimental 2T–CT data for the initial and embrittled RPV 2Cr–Ni–Mo–V steels for WWER-1000 is performed.

On the process zone of a quasi-static growing tensile crack with power-law elastic-plastic damage*

Parametric studies are made on the growing crack tip fields under quasi-static tensile loading with damage coupled power-law elastic-plastic constitutive equations. A two-sector demarcation scheme is used. The asymptotic orders and angular distributions of the stress and damage fields are obtained. The shapes of the process zone are also determined. The law of crack growth is formulated as well.

A discrete dislocation analysis of mode I crack growth

Small scale yielding around a plane strain mode I crack is analyzed using discrete dislocation dynamics. The dislocations are all of edge character, and are modeled as line singularities in an elastic material. At each stage of loading, superposition is used to represent the solution in terms of solutions for edge dislocations in a half-space and a complementary solution that enforces the boundary conditions. The latter is non-singular and obtained from a finite element solution. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. A relation between the opening traction and the displacement jump across a cohesive surface ahead of the initial crack tip is also specified, so that crack growth emerges naturally from the boundary value problem solution. Material parameters representative of aluminum are employed. For a low density of dislocation sources, crack growth takes place in a brittle manner; for a low density of obstacles, the crack blunts continuously and does not grow. In the intermediate regime, the average near-tip stress fields are in qualitative accord with those predicted by classical continuum crystal plasticity, but with the local stress concentrations from discrete dislocations leading to opening stresses of the magnitude of the cohesive strength. The crack growth history is strongly affected by the dislocation activity in the vicinity of the growing crack tip.

Dynamic Scaling for Kinetic Cluster Formation in Random Growth Process

The dynamic properties of surface crack growth are investigated through the time endent cluster size distribution function and scaling theory. Several curves of the time-dependent cluster size distribution at times A growing crack and growing crack tip are selected randomly in each time step (one unit of time step is increased when one bond is broken, i.e., the cluster size of crack increases by one). A crack can grow only from the growing lattice point and the growth of the crack is allowed to any adjacent lattice points, but which is inhibited from crossing over its own trace of growing crack (self-avoiding). Usually the cracks cannot grow indefinitely in an actual material by stress relaxation at the tip of a crack and lowering of hydrogen pressure in the crack cavity. The conditions for cessation of crack growth in this model are as follows: (1) A growth point of a crack reaches to an adjacent crack (Link). (2) A growth point is trapped in its own cluster (Selftrapping). (3) A growth point reaches to an edge of the lattice (Edge-relaxation). Figure 2 shows crack growth patterns of 100×100 of the lattice plane size. The initial defects shown by closed circles are randomly distributed on a bottom edge of the square lattice points. In this model, growth probability of each crack tip to x-direction is assumed to be 1 (PRIP=PRIM=1) and plus y-direction to be 1 (PRJP=1), minus y-direction to be 0.1 (PRJM=0.1). PRIP and PRIM are the growth probability to plus xdirection and minus x-direction, and PRJP and PRJM are the growth probability to plus y-direction and minus y-direction, respectively. In this case, two clusters link up and form a large cluster. The clusters continue to grow in the same manner in a self-avoiding random walk until they satisfy the cessation conditions. Figure 3 shows crack growth patterns of 200×200 of the lattice plane size and the number of initial defects is 20. The growth probability of each crack tip is assumed to be PRIP=PRIM=PRJP=1 and PRJM=0.1. This figure shows the crack patterns when all clusters ceased to grow. The temporal evolution of crack patterns at the time t = 100, 600, 1400 and 1943 are shown in Fig. 4. The system is 200×200 of square lattice and the number of initial defects is 20. In this case, the clusters ceased to grow at the time t = 1943.

Interface Debonding Behavior and Its Effect on Crack Stability in PMMA/Glass Bi-Material

Interface debonding and its effect on crack stability in a single-edge-notched PMMA/glass bi-material have been studied. Direct observation of crack growth behavior is carried out and crack tip stress intensity factor during crack growth process is obtained by a laser Caustics method. Interface stress distribution at the onset of interface debonding is obtained by FEA with experimentally obtained stress/strain conditions. The interface debonding ahead of a growing crack tip occurs before the crack reaches the interface. A transition from slow to rapid crack growth is predicted by the event of an interface debonding ahead of a growing crack tip. This debonding is caused by an interface tensile stress. The maximum interface tensile stress obtained by FEA with experimental boundary condition, σd, and the distance between the crack tip and interface at the onset of interface debonding, x0, follows the relation, σd=Ad⁄\sqrtx0. This relation provides the condition for the interface tensile debonding. The condition suggests that the interface tensile debonding has a probabilistic nature.

Effect of materials variables on the tear behaviour of a non-crystallising elastomer

Crack growth rates (r) were measured in pure shear test specimens as a function of strain energy release rate (G) for a non-crystallising SBR elastomer. Measurements were made as a function of: extent of swelling with Dibutyl Adipate; carbon black content; and crosslink density. In some cases experiments were carried out over a range of temperatures. In most cases the resulting G versus r plots showed a clear transition from rough to smooth crack surface behaviour with increasing crack growth rate, with an intervening slip/stick region. In the high speed/steady tear/smooth region the value of G necessary to drive a crack at a given rate was determined largely by the magnitude of the visco-elastic losses in the crack tip region, increasing with: decreasing temperature; increasing molar mass between crosslinks; decreasing extent of swelling; and increasing carbon black content. However G was independent of specimen thickness in this region suggesting that crack tip effects were minimal. In the low speed/rough region changes in the magnitude of G with materials and temperature/rate variables could not be explained by changes in visco-elastic loss alone. Furthermore the magnitude of G increased significantly with increasing specimen thickness. This suggested that in this region cavitation ahead of the growing crack tip resulting from dilatational stresses determined the crack tip diameter, and hence the magnitude of G.