Showing papers on "Crack closure published in 1995"

Fracture Criteria for Piezoelectric Ceramics

Abstract: Fracture criteria for piezoelectric materials were investigated. Mode I and mixed mode fracture tests were performed on PZT-4 piezoelectric ceramics to verify the validity of the mechanical strain energy release rate as a fracture criterion. Experimental results indicated that crack extension could be aided or impeded by an electric field, depending on the field direction. Further, the direction of crack extension was studied. A crack closure method, together with finite element analysis, was introduced to calculate the mechanical strain energy release rate. The maximum mechanical strain energy release rate was used to predict fracture loads under combined mechanical and electrical loads. It was found that the mechanical strain energy release rate criterion is superior to other fracture criteria and predicts fracture loads fairly accurately.

Ductile crack growth-I. A numerical study using computational cells with microstructurally-based length scales

Abstract: Many metals which fail by a void growth mechanism display a macroscopically planar fracture process zone of one or two void spacings in thickness characterized by intense plastic flow in the ligaments between the voids; outside this region, the voids exhibit little or no growth. To model this process a material layer containing a pre-existing population of similar sized voids is assumed. The thickness of the layer, D, can be identified with the mean spacing between the voids. This layer is represented by an aggregate of computational cells of linear dimension D. Each cell contains a single void of some initial volume. The Gurson constitutive relation for dilatant plasticity describes the hole growth in a cell resulting in material softening and, ultimately, loss of stress carrying capacity. The collection of cells softened by hole growth constitutes the fracture process zone of length l1. Two fracture mechanism regimes can be identified corresponding to l1 ≈ D and l1 ⪢ D. The connection between these mechanisms and fracture resistance is discussed. Finite element calculations have been carried out to determine crack growth resistance curves for plane strain, mode I crack growth under small scale yielding. A row of voided cells is placed on the symmetry plane ahead of the initial crack. These cell elements are embedded within a conventional elastic-plastic continuum. Under increasing load, the voids in the cells grow and coalesce to form a new crack surface thereby advancing the crack. Resistance curves are calculated for crack growth exceeding many multiples of D. The parameters affecting fracture resistance are discussed emphasizing the roles of microstructural parameters and continuum properties of the material. The effect of crack tip constraint on fracture resistance is examined under small scale yielding by way of the T-stress. As a final application, resistance curves for a deep and a shallow crack bend bar are computed. These are compared with experimental data.

A computational approach to ductile crack growth under large scale yielding conditions

Abstract: Mode I crack initiation and growth under plane strain conditions in tough metals is computed using an elastic-plastic continuum model which accounts for void growth and coalescence ahead of the crack tip. The material parameters are the Young’s modulus, yield stress and strain hardening exponent of the metal, along with the parameters characterizing the spacing and volume fraction of voids in material elements lying in the plane of the crack. For a given set of these parameters and a specific specimen, or component, subject to a specific loading, relationships among load, load-line displacement and crack advance can be computed with no restrictions on the extent of plastic deformation. Similarly, there is no limit on crack advance, except that it must take place on the symmetry plane ahead of the initial crack. Suitably defined measures of crack tip loading intensity, such as those based on the J-integral, can also be computed, thereby directly generating crack growth resistance curves. In this paper, the model is applied to five specimen geometries which are known to give rise to significantly different crack tip constraints and crack growth resistance behaviors. Computed results are compared with sets of experimental data for two tough steels for four of the specimen types. Details of the load, displacement and crack growth histories are accurately reproduced, even when extensive crack growth takes place under conditions of fully plastic yielding.

Effects of microstructure on the deformation and fracture of γ-TiAl alloys

Abstract: Deformation and fracture behavior of two-phase γ-TiAl alloys were investigated under monotonic tension loading conditions for duplex and lamellar microstructural forms. The effects of microstructure on tensile properties and deformation-fracture behavior are analyzed for deformation temperatures below and above the brittle-ductile transition. The crack initiation toughness and associated strains near the crack tip are used to explain the inverse relationship between ductility and toughness observed at room temperature. Fracture resistance behavior and toughening mechanisms at room temperature are explained in terms of microstructure and deformation anisotropy. The competition between the effects of grain size and lamellar spacing or tensile and toughness properties is discussed.

Fracture simulations using large-scale molecular dynamics

Abstract: We report on recent molecular-dynamics (MD) fracture simulations of mode-I tensile loading at high strain rates. Because cracks emit sound waves, previous simulations became unreliable beyond one sound traversal time. Using massively parallel MD, we show how to eliminate unwanted boundary effects and study unimpeded crack propagation mechanisms. In order to represent tensile stress conditions near the crack tip, we employ uniaxial, homogeneously expanding periodic boundary conditions, examining the effects of strain rate, temperature, and interaction potential. Because our samples are sufficiently large, we see dislocations being emitted from the crack tip at nearly the shear-wave sound speed ${\mathit{c}}_{\mathit{s}}$. As they move many lattice spacings away from the crack, they slow down, finally moving at about 2/3${\mathit{c}}_{\mathit{s}}$. Each time dislocations are emitted, the crack tip ``fishtails,'' and at sufficiently high strain, the crack can fork; dislocations can climb and become nucleation sites for additional microcracks. We find that we can suppress ductile behavior by including viscous damping in the equations of motion, thereby demonstrating a transition to brittle crack propagation as static, zero-strain-rate conditions are approached. Finally, we show that, by altering only the attractive tail of the pair potential, we can change a ductile material into a brittle one. Under dynamic crack propagation, the distinction between ductile and brittle behavior is blurred: in brittle materials, dislocations are asymptotically bound to the crack tip, while in ductile materials, they can escape.

Fracture normal to a bimaterial interface: Effects of plasticity on crack-tip shielding and amplification

Abstract: The problem of a crack approaching a bimaterial interface is considered in this paper. Attention is focused on an interface between two elastoplastic solids whose elastic properties are identical and whose plastic properties are different. For the case of a crack approaching a bimaterial interface perpendicularly, it is shown by recourse to detailed finite element analyses that the near-tip “driving force” for fracture is strongly influenced by whether the crack approaches the interfaces from the lower strength or the higher strength materials. Specifically, it is demonstrated that the crack-tip is “shielded” from the remote loads when it approaches the interface from the weaker material, and that the effective J-integral at the crack tip is greater than the remote J when it approaches the interface from the stronger material. This plasticity effect determines whether a crack approaching the bimaterial interface continues to advance through the interface or is arrested before penetrating the interface. These theoretical findings are substantiated using controlled experiments of fatigue crack growth perpendicular to a ferrite—austenite bimaterial interface. The effect of the non-singular T-stress, acting parallel to the crack plane, on shielding and amplification of the stress fields is also discussed.

Ductile crack growth—II. Void nucleation and geometry effects on macroscopic fracture behavior

Abstract: Many metals that fail by void growth and coalescence display a macroscopically planar fracture process zone of one or two void spacings in thickness; outside this region, the voids exhibit little or no growth. A finite element model of this mode of failure was described in Part I of this paper [J. Mech. Phys. Solids, 43, 233–259 (1995)]. A row of void-containing cell elements is placed on the symmetry plane ahead of the initial crack. The cells incorporate the softening characteristics of hole growth and dependence on stress triaxiality. These cells are embedded within a conventional elastic-plastic continuum. Under increasing strain, the voids grow and coalesce to form new crack surfaces, thereby advancing the crack. Parametric studies reveal that the important microstructural parameters in the model are D and f0, characterizing the spacing and the initial volume fraction of voids on the fracture plane. Using this model, Xia et al. [J. Mech. Phys. Solids, 43, 389–413 (1995)] have successfully predicted details of the load, displacement and crack growth histories—collectively referred to as the macroscopic fracture behavior—of four specimen geometries, which give rise to significantly different crack tip constraints under fully plastic conditions. Here we study the quantitative effects of void nucleation by a stress and strain criterion on the macroscopic fracture behavior. This behavior is compared with predictions using a similar volume of voids present from the very beginning. Geometry effects on macroscopic fracture behavior under contained and fully yielded conditions are discussed for the three-point-bend specimen and the center-crack-panel loaded in tension. Here the objective is to show the connection between the crack growth resistance and the fracture environment, namely, the constraint ahead of the crack tip and the tensile stress on the fracture plane.

Bimaterial interfacial crack growth as a function of mode-mixity

Abstract: The mechanical integrity of many electronic devices and their components is determined by the strength of the interfaces between dissimilar materials. Therefore, the knowledge of interfacial strength is important to the design for reliability of these devices. A few examples are die/die attach interface, leadframe/molding compound interface, and copper/resin interfaces in multilayer printed circuit boards. Failure of these interfaces results in reduced reliability and performance of such electronic devices. Two important issues are raised in terms of applying the interfacial fracture to the bimaterial interface reliability prediction. The first issue is the quantification of strength (fracture toughness) in such interfaces as a function of mode mixity. The second issue is the computing of actual energy release rate (a generalized crack driving force) and comparing it with the measured fracture toughness so as to predict the crack initiation, growth, and failure of electronic devices. This study emphasizes on a unified methodology and demonstrates the feasibility of application of the rigorous interfacial fracture mechanics for the delamination growth. The proposed numerical scheme was verified by three examples: a DCB unidirectional composite beam, a DCB resin/copper beam, and an ENF resin/copper beam. Using a crack closure technique, the energy release rate and mode mixity are evaluated and used to predict the behavior of the specimens before and after delamination growth. Good agreement between testing and prediction has been achieved. >

Shear dominated transonic interfacial crack growth in a bimaterial-i. experimental observations

Abstract: In this work we describe a series of impact experiments performed on PMMA/4340 steel edge cracked bimaterial plates Specimens were impacted at 20 m s−1 in a one point bend configuration using a high speed gas gun Dynamic interfacial crack propagation was observed using the optical method of Coherent Gradient Sensing and high speed photography Very high crack tip accelerations (108 m s−2) and very high crack tip speeds (up to 15cRPMMA) were measured and are reported Quantitative measurements show that in experiments in which the crack tip speed entered the intersonic range for PMMA, the stress field surrounding the crack tip was shear dominated The observation of high shear around the crack tip can also be explained using wave propagation arguments It is found that the reason for attainment of intersonic (with respect to PMMA) crack tip speeds is directly related to the large amounts of energy necessary to initiate the crack tip under shear dominated conditions A comparison with the theoretical results of Part II in this study is also made There seems to be an unfavorable region of stable crack propagation velocities in the intersonic regime This region is cspmma < v < √2csPMMA In all experiments performed, the propagating crack accelerated quickly out of this region In the few interferograms that do actually correspond to crack propagation in this unfavorable velocity range, crack face contact was observed This observation is also in agreement with the findings of Part II of this investigation

Shear dominated transonic interfacial crack growth in a bimaterial I-II. Asymptotic fields and favorable velocity regimes

Abstract: Motivated by experimental observations of transonic crack tip speeds (Lambros and Rosakis, 1994c, J. Mech. Phys. Solids 43(2), 169–188), the problem of intersonic interfacial crack growth in an elastic-rigid bimaterial system is analysed. Following the analytical procedure employed in Liu et al. (1993, J. Mech. Phys. Solids 41, 1887–1954), the two-dimensional in-plane asymptotic deformation field surrounding the tip of a crack propagating intersonically along an elastic-rigid bimaterial interface, is obtained. The theoretical results show that the near-tip stress field does not exhibit oscillations, while a stress singularity weaker than 0.5 still exists and is a function of the crack tip speed. In addition, due to the intersonic nature of crack growth, a singular line emanating from the moving crack tip is present in the near-tip field. Across this line, stresses and particle velocities suffer infinite jumps. The theoretical analysis also shows that the near-tip deformation field is shear dominated. It is also shown that in the velocity range cs < v < √2cs, either crack face contact or negative normal tractions ahead of the crack tip exist. Visual evidence of such contact is reported in Part I of this study. These observations, together with additional experimental results of Part I, lead to the conclusion that crack growth is favorable in the velocity regimes 0 < v < cs and √2cs < v < c1.

A model for dynamic embrittlement

Abstract: A model is presented to calculate the rate of crack advance in the stepwise decohesion process which can result from the stress-induced penetration of a surface-adsorbed element into a solid, usually along grain boundaries. We call this process dynamic embrittlement. The model employs a diffusion equation containing both the usual random-mixing term and a term reflecting the work done by a tensile stress when surface atoms diffuse inward. Given the diffusion constant of the surface species and the stress profile at the crack tip, the concentration build-up ahead of the crack as a function of time can be calculated. This can be combined with an empirical relationship between the interfacial concentration of the surface species and the stress to cause decohesion to give the crack-growth rate. This model is applied to the case of sulfur-induced cracking of an alloy steel in the process known as stress-relief cracking.

Classification of fatigue crack growth behavior

Abstract: A self-consistent theory has been developed to account for the variation in fatigue crack growth rates with load ratio,R, without reference to crack closure concepts. The theory states that (a) for an unambiguous description of cyclic damage, two loading parameters are required; (b) consequently, there are two thresholds corresponding to each parameter that must be satisfied for a crack to grow; (c) these two thresholds are intrinsic and are independent of specimen geometry; (d) a fundamental threshold curve can be developed that is independent of test methods defining these two thresholds from the asymptotic values, and last; (e) the two thresholds vary with the degree of slip planarity, microstructure, and environment. Based on these new concepts, we have classified the entire fatigue crack growth behavior into five different classes using the experimental ΔKth-R data. The characteristic feature of each class is discussed, and the supporting examples of materials behavior are provided. This classification could provide a basis for understanding the synergistic effects of mechanical and chemical driving forces and microstructure contributing to fatigue crack growth.

A Backface Strain Technique for Detecting Fatigue Crack Initiation in Adhesive Joints

Abstract: A new backface strain technique was developed to detect fatigue crack initiation in adhesive-bonded lap joints. The technique was based on the special strain distribution in single lap joints and detected the fatigue crack initiation by the switch in the direction of the strain variation. Use of this technique not only permits the determination of fatigue crack initiation life in the joint, but also allows the site of crack initiation to be located. With the assistance of this new backface strain technique, a fatigue crack was found to initiate in the adhesive but to propagate towards the interface to continue its growth on the interface and to cause the final separation of the joint along the interface. Measurements of fatigue crack initiation lives at different stress levels indicate that the adhesive-controlled crack initiation took an increasingly greater proportion of the total fatigue life as the stress decreased, so that the lifetime in the long-life regime was dominated by the resistance ...

Three-Dimensional CTOA and Constraint Effects During Stable Tearing in a Thin-Sheet Material

Abstract: A small strain theory, three-dimensional elastic-plastic finite element analysis was used to simulate fracture in thin sheet 2024-T3 aluminum alloy in the T-L orientation. Both straight and tunneled cracks were modeled. The tunneled crack front shapes as a function of applied stress were obtained from the fracture surface of tested specimens. The stable crack growth behavior was measured at the specimen surface as a function of applied stress. The fracture simulation modeled the crack tunneling and extension as a function of applied stress. The results indicated that the global constraint factor, alpha(sub g), initially dropped during stable crack growth. After peak applied stress was achieved, alpha(sub g) began to increase slightly. The effect of crack front shape on alpha(sub g) was small, but the crack front shape did greatly influence the local constraint and through-thickness crack-tip opening angle (CTOA) behavior. The surface values of CTOA for the tunneled crack front model agreed well with experimental measurements, showing the same initial decrease from high values during the initial 3mm of crack growth at the specimen's surface. At the same time, the interior CTOA values increased from low angles. After the initial stable tearing region, the CTOA was constant through the thickness. The three-dimensional analysis appears to confirm the potential of CTOA as a two-dimensional fracture criterion.

Crack instabilities of a heated glass strip.

Abstract: Recently, Yuse and Sano [Nature (London) 362, 329 (1993)] have observed that a crack traveling in a glass strip submitted to a nonuniform thermal diffusion field undergoes numerous instabilities. We study two cases of quasistatic crack propagation. The crack extension condition in straight propagation is determined. An asymptotic analysis of the elastic free energy is introduced and scaling laws are derived. A linear stability analysis of the straight propagation is performed, based on the assumption that the crack tip propagation deviates from the centered straight one as soon as it is submitted to a ``physical'' singular shear stress. It is shown that a straight propagation can become unstable after which a wavy instability appears. The condition for instability as well as the selected wavelength is calculated quantitatively. The results are compared with experiments and the agreement is favorable.

Effects of local constraint along three-dimensional crack fronts—a numerical and experimental investigation

Abstract: A two-parameter characterization of the crack front state in a variety of geometries (mode I) is explored by means of three-dimensional finite element analysis, including finite strain effects. In particular the approximate J-Q theory is scrutinized and it is found that Q appears to be a good measure of the deviation in stress triaxiality ahead of a crack tip as compared to the highly constrained plane strain SSY-solution, also in cases where the crack front is relatively curved. The implications for cleavage fracture in the upper transition region are elucidated by appraising the results from an extensive experimental program, where both tension and bending type of plane specimens as well as surface cracked plate specimens had been tested. It appears that the J-Q concept together with some cleavage failure criteria, e.g. the RKR-model, can be applied locally along three-dimensional crack fronts in a structure in order to assess cleavage fracture. To the extent that one dominating cleavage fracture spot could be located at a three-dimensional crack border, this was in general found at the position which had undergone the most critical J-Q sequence, in the light of the RKR-criteria. Microstructural features of both ductile and cleavage fracture are elucidated by a fractographical survey performed.

Finite element calculation of stress intensity factors for interfacial crack using virtual crack closure integral

Abstract: This paper presents a successful implementation of the virtual crack closure integral method to calculate the stress intensity factors of an interfacial crack. The present method would compute the mixed-mode stress intensity factors from the mixed-mode energy release rates of the interfacial crack, which are easily obtained from the crack opening displacements and the nodal forces at and ahead of the crack tip, in a finite element model. The simple formulae which relate the stress intensity factors to the energy release rates are given in three separate categories: an isotropic bimaterial continuum, an orthotropic bimaterial continuum, and an anisotropic bimaterial continuum. In the example of a central crack in a bimaterial block under the plane strain condition, comparisons are made with the exact solution to determine the accuracy and efficiency of the numerical method. It was found that the virtual crack closure integral method does lead to very accurate results with a relatively coarse finite element mesh. It has also been shown that for an anisotropic interfacial crack under the generalized plane strain condition, the computed stress intensity factors using the virtual crack closure method compared favorably with the results using the J integral method applied to two interacting crack tip solutions. In order for the stress intensity factors to be used as physical variables, the characteristic length for the stress intensity factors must be properly defined. A study was carried out to determine the effects of the characteristic length on the fracture criterion based the mixed-mode stress intensity factors. It was found that the fracture criterion based on the quadratic mixture of the normalized stress intensity factors is less sensitive to the changes in characteristic length than the fracture criterion based on the total energy release rate along with the phase angle.

Development of a Dynamic Decohesion Criterion for Subsonic Fracture of the Interface between Two Dissimilar Materials

Abstract: We present findings of an experimental study of dynamic decohesion of bimaterial systems composed of constituents with a large material property mismatch Poly-methylmethacrylate (PMMA)-steel and PMMA-aluminium bimaterial fracture specimens were used Dynamic one-point bend loading was accomplished with a drop-weight tower device (for low and intermediate loading rates) or a high-speed gas gun (for high loading rates) High-speed interferometric measurements were made using the lateral shearing interferometer of coherent gradient sensing in conjunction with high-speed photography Very high crack propagation speeds (terminal crack-tip speeds up to 15c_s^(PMMA), where c_s^(PMMA) is the shear wave speed of PMMA) and high accelerations (of about 10^7g, where g is the acceleration of gravity) were observed and are reported Issues regarding data analysis of the high-speed interferograms are discussed The effects of near-tip three-dimensionality are also analysed Dynamic complex stress factor histories are obtained by fitting the experimental data to avail-able asymptotic crack-tip fields A dynamic crack growth criterion for crack growth along bimaterial interfaces is proposed In the subsonic regime of crack growth it is seen that the opening and shearing displacements behind the propagating crack tip remain constant and equal to their value at initiation, ie the crack retains a self-similar profile during crack growth at any speed This forms the basis of the proposed dynamic interfacial fracture criterion

Cyclic Fatigue in Ceramics: A Balance between Crack Shielding Accumulation and Degradation

Abstract: Cyclic fatigue growth rates in R-curve ceramics have been observed to depend very strongly on the maximum applied stress intensity, K{sub max}, and only weakly on the stress intensity range, {Delta}K. This behavior is rationalized through measurement of crack wake shielding characteristics as a function of these fatigue parameters in a gas-pressure-sintered silicon nitride. In particular, evidence for a mechanical equilibrium between shielding accumulation by crack growth and shielding degradation by frictional wear of sliding interfaces is found for steady-state cyclic fatigue. This equilibrium gives rise to a rate law for cyclic fatigue. The data suggest that the accumulation process is the origin of the strong K{sub max} dependence, and that the degradation process is the origin of the weak {Delta}K dependence. These features are shown to be related to the ``cyclic`` R-curve and to the cyclic crack opening displacement, respectively.