Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to crack initiation, the crack speed history and the crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal crack speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main crack off the bond line into the PMMA occurs, together with micro-crack nucleation on the bond line. The crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the crack progressively drifting further into the PMMA.     

Crack deflection at an interface of alumina/metal joint: A numerical analysis

Deflection of a crack at the bimaterial interface is the initial mechanism required for obtaining enhanced toughness in bimaterial system. In this paper, a criterion is presented to predict the competition between crack deflection and penetration at the interface, using an energy release rate criterion. The finite element methods are used to calculate the strain energy release rates at the crack tip of alumina–metal bimaterial that either deflect or penetrate at the interface as a function of elastic mismatch and length of the deflected or penetrated crack. The effects of the elastic properties of two bonded materials were highlighted in order to evaluate the conditions for the crack deflection by the interface as well as the distance between the crack tip and the interface.     

Dynamic fields generated by rapid crack growth

Stresses and strains near a rapidly propagating crack tip are affected by the mass density of the material. This paper starts with a brief summary of analytical results for near-tip dynamic fields as predicted by linear elastic fracture mechanics. Next, exact expressions are derived for dynamic crack-line strains, for mode-III crack propagation in a nonlinear elastic material and in an elastic perfectly-plastic material. These expressions are valid on the crack line from the moving crack tip to the moving boundary with the region of linearly elastic deformation. For steady-state crack growth, a critical strain criterion is used to compute the relation between external load and crack tip speed. The required external load increases with crack-tip speed.     

Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.     

Transient thermoelastic fracture of interface cracks: Effect of bending restraints

The behavior of an interface crack at the center and at the edge of a restrained, bimaterial structure subjected to transient thermal loads is studied. A linear, elastic fracture analysis is used to determine the effects of material property and layer thickness ratio on the transient strain energy release rates. Quantitative comparisons for a range of moduli one order of magnitude either side of equality are tabulated for equal sized material on either side of the crack in terms of the near tip displacements and strain energy release rates.     

Crack-tip fields for matrix cracks between dissimilar elastic and creeping materials

The stress fields near the tip of a matrix crack terminating at and perpendicular to a planar interface under symmetric in-plane loading in plane strain are investigated. The bimaterial interface is formed by a linearly elastic material and an elastic power-law creeping material in which the crack is located. Using generalized expansions at the crack tip in each region and matching the stresses and displacements across the interface in an asymptotic sense, a series asymptotic solution is constructed for the stresses and strain rates near the crack tip. It is found that the stress singularities, to the leading order, are the same in each material; the stress exponent is real. The oscillatory higher-order terms exist in both regions and stress higher-order term with the order of O(r°) appears in the elastic material. The stress exponents and the angular distributions for singular terms and higher order terms are obtained for different creep exponents and material properties in each region. A full agreement between asymptotic solutions and the full-field finite element results for a set of test examples with different times has been obtained.     

On the influence of a bimaterial interface on dynamic stress intensity factors

Summary The method of dynamic Green's function and the integral transforms are applied to investigate the elasto-dynamic stress intensity factor of a crack straddling an interface of a bimaterial composite. The crack which extends to infinity on one side is assumed to extend an arbitrary distancea on the other side of the interface. Anti-plane line loads are suddenly applied at timet=0 on either side of the crack surface at arbitrary distancesl ₁ andl ₂ from the interface. The effect of the interface on the dynamic stress field near the crack tip is studied. It is found that the transmitted wave through the interface and reflected wave from the interface serve to increase or decrease the stress field in the vicinity of the crack tip depending on the elastic properties of the two materials.     

An analytical expression for the J2‐integral of an interfacial crack in orthotropic bimaterials

This paper presents a new analytical expression relating the J₂‐integral and stress intensity factors (SIF) in an in‐plane traction‐free crack between two orthotropic elastic solids using the complex function method. The singular oscillatory near tip field of a bimaterial interfacial crack is usually characterized by a pair of SIFs. In linear elastic interfacial fracture mechanics, the majority of numerical and experimental methods rely on the analytical equations relating J_k‐integrals and SIFs. Although an analytical equation relating J₁‐integral or strain energy release rate and SIFs is available, a similar relation for J₂‐integral in debonded anisotropic solids is non‐existent. Using this new analytical expression, in conjunction with the values of J_k, the SIFs can be computed without the need for an auxiliary relation. An example with known analytical solutions for SIFs is presented to show the variation of the J₂‐integral near the crack tip of a bimaterial orthotropic plate. Different bimaterial combinations are considered, and the effect of material mismatch on J_k is demonstrated.     

Numerical analysis of blunting of a crack tip in a ductile material under small-scale yielding and mixed mode loading

The blunting of the tip of a crack in a ductile material is analysed under the conditions of plane strain, small-scale yielding, and mixed mode loading of Modes I and II. The material is assumed to be an elastic-perfectly plastic solid with Poisson's ratio being 1/2. The stress and strain fields for a sharp crack under mixed mode loading are first determined by means of elastic-plastic finite element analysis. It is shown that only one elastic sector exists around the crack tip, in contrast with the possibility of existence of two elastic sectors as discussed by Gao. The results obtained for a sharp crack are used as the boundary conditions for the subsequent numerical analysis of crack tip blunting under mixed mode loading, based on slip line theory. The characteristic shapes of the blunted crack tip are obtained for a wide range of Mode I and Mode II combinations, and found to resemble the tip of Japanese sword. Also the stress field around the blunted crack tip is determined.     

Dynamic fracture of a beam or plate under tensile loading

The dynamic fracture response of a long beam of brittle elastic material under tensile loading is studied. If the magnitude of the applied loading is increased to a critical value, a crack is assumed to propagate across the beam cross section. In a parallel analysis to [t] the crack length and applied loading at the fracture face are determined as functions of time measured from fracture initiation. The results of the analysis are shown in graphs of crack length, crack tip speed and fracturing section tensile loading vs time. As found in [1], the crack tip accelerates very quickly to a speed near the characteristic terminal speed for the material, travels at this speed through most of the beam thickness, and then decelerates rapidly in the final stage of the process. Finally, by appropriate change of the elastic modulus, the results may be applied to plane strain fracture of a plate under pure tensile loading.     

Crack growth on elastic-plastic bimaterial interfaces

Finite element calculation based on finite strain theory is carried out to simulate the crack growth on bimaterial interfaces under the assumption of small scale yielding and plane strain condition. The modified Gurson's constitutive equation and the element vanish technique introduced by Tvergaard et al. are used to model the final formation of an open crack. The crack growths in homogeneous material and in bimaterials are compared. It is found from the calculation that the critical macroscopic fracture toughness for crack growth J _IC is much lower in bimaterials than in homogeneous material. For bimaterial cases, the J _IC of a crack between two elastic-plastic materials which have identical elastic properties with different yield strength is lower than that of a crack between an elastic-plastic material and a rigid substrate. It seems that the difference in yield strength between the dissimilar materials has more significant influence on the void nucleation and crack growth than the difference in hardening exponent.     

Transient dislocation emission from a crack tip in an anisotropic elastic material

The emission of a dislocation with a general Burgers vector from the tip of a stationary semi-infinite crack in an anisotropic elastic material is examined. The dislocation is assumed to leave the crack tip along the crack extension plane at constant speed. Explicit expressions for the transient shielding stress intensity factors at the crack tip and the drag forces on the dislocations are derived. Numerical results for a class of cubic materials and two hexagonal crystals, zinc and cobalt, are given. Dislocation emission under plane stress wave loading is discussed.     

Effect of a graded layer on the plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

Prior work by the authors has proposed a dissipated energy theory of fatigue crack growth in ductile solids under mode I loading based on the total plastic dissipation per cycle ahead of the crack. The approach has since been extended to a general bimaterial interface geometry under mixed-mode I/II loading, with application to fatigue debonding of layered materials. An inherent assumption of this prior work is that a perfect crack exists along the interface between the two materials. The current work extends the approach to incorporate a grading of material properties between the two layers, as may occur in a variety of welding, soldering or layered manufacturing applications. Attention is restricted to elastic perfectly-plastic layers with identical elastic properties and a mismatch in yield strength across a linearly graded interface, with the crack on the boundary of the weaker material. A dimensionless plastic dissipation is extracted from 2-D plane strain finite element models over the full range of yield strength mismatches, graded layer thicknesses and mixed-mode loading conditions. Results reveal that for all modes of loading, the effect of a graded layer is to increase the total plastic dissipation per cycle, which is bounded by the extremes in plastic mismatch for a perfect crack interface. While the graded layer has a measurable effect, the plastic dissipation for all strength mismatches is dominated by the mode of loading.     

EFFECT OF ELASTIC MISMATCH ON THE GROWTH OF A CRACK INITIALLY TERMINATED AT AN INTERFACE IN ELASTIC PLASTIC BIMATERIALS

Abstract A crack perpendicular to, and initially with the tip on, a bimaterial interface is studied. An asymptotic analysis is performed and crack growth proceeds straight ahead at constant remote load. Mode I conditions and plane strain are assumed. The materials on both sides of the interface are elastic perfectly-plastic with different elastic properties and the same yield stress. A finite element analysis is made and crack growth is simulated by an element relaxation technique. Because of the interface, the crack-tip driving force is not constant, which is reflected in the near-tip state. The development of the plastic zone and the crack opening displacements is presented for different elastic mismatches. Small scale yielding like results are obtained after a crack extension of about the plastic zone size from the interface, i.e. long before a square-root singular stress field may be expected to embed the plastic zone. An important observation is that the development of the crack opening displacement at the initial stage of growth is reversed when plasticity is introduced, as compared to the prediction by an elastic model. A region of stable crack growth is identified at the initial phase of growth into a stiffer material, solely due to elastic mismatch.     

Effect of loading and geometry on the subsonic/intersonic transition of a bimaterial interface crack

An experimental investigation was conducted to study the nature of intersonic crack propagation along a bimaterial interface. A single edge notch/crack oriented along a polymer/metal interface was loaded predominantly in shear by impacting the specimen with a high velocity projectile fired from a gas gun. The stress field information around the propagating crack tip was recorded in real time by two different optical techniques--photoelasticity and coherent gradient sensing, in conjunction with high speed photography. Intersonic cracks on polymer/metal interfaces were found to propagate at speeds between the shear wave speed (c_s) and of the polymer. The nature of the crack tip fields during subsonic/intersonic transition and the conditions governing this transition were examined. Experimental observations showed the formation of a crack face contact zone as the interfacial crack speed exceeds the Rayleigh wave speed of the polymer. Subsequently, the contact zone was observed to expand in size, shrink and eventually collapse onto the intersonic crack tip. The recorded isochromatic fringe patterns showed multiple Mach wave formation associated with such a scenario. It is found that the nature of contact zone formation as well as its size and evolution differ substantially depending on the sign of the opening component of loading.     

Fracture toughness of selectively reinforced Al2124 alloy: precrack tip in the aluminium alloy side

Abstract

The fracture toughness of Al2124/Al2124+SiC bimaterials is affected by thermal residual stresses, elastic/plastic mismatch, precrack tip position, and failure mechanism. When the precrack tip is in the Al2124 side, final catastrophic failure occurs when ductile fracture of the Al2124 layer between the precrack tip and the composite side takes place, followed by fracture of the composite layer. For a precrack tip 2·0 mm from the interface, K _Q(5%) values are lower than the 'Al2124 only' value due to the near crack tip tensile residual stresses and higher stress triaxiality within the Al alloy ligament. At 0·5 mm from the interface, K _Q(5%) values increase and are usually as high as the 'Al2124 only' value due to the stronger shielding of the elastic/plastic mismatch. If the precrack tip is 2·0 mm from the interface, K _crit values of the bimaterial are higher than the 'Al2124 only' value and this is deduced to be due to the elastic/plastic mismatch shielding. At 0·5 mm from the interface, K _crit values are reduced because both the near tip tensile residual stress is higher and stress triaxiality levels of the ductile ligament are higher, although the elastic/plastic mismatch shielding is also higher at this position.     

An elastic-plastic finite element analysis of a blunting interface crack with microvoid damage

A finite strain elastic-plastic finite element analysis is performed on a crack which lies on an interface between two dissimilar materials. The materials above and below the interface are assumed to be different from each other in yield stress or in strain-hardening exponent. Gurson's constitutive equation for porous plastic materials is used in order to take into account the effect of the microvoid nucleation and growth on the fields near the tip of a crack.It is found that the microvoids have larger effects on the crack tip blunting and stress fields for a bimaterial than for a homogeneous material. It is also found that the plastic strain and the microvoid volume fraction localize in a few narrow bands which grow into the softer material from the intersection of the interface and the blunted crack tip at inclinations of about 15° 45°.     

INTERFACIAL CRACK INITIATION UNDER QUASI-STATIC AND DYNAMIC LOADING CONDITIONS: AN EXPERIMENTAL STUDY

Abstract— Interfacial fracture parameters under quasi-static and dynamic loading are examined in a large elastic mismatch bimatenal system. A wide range of remote field loading ratios of shear and tension are considered. The crack tip fields are mapped using the optical method of coherent gradient sensing or CGS and fracture parameters are quantified. Distinctly different crack initiation responses are observed for positive and negative shear stresses acting on the interface. Also, low velocity impact loading experiments are conducted to study the influence of dynamic loading on crack initiation parameters. Dynamic interfacial crack tip fields are recorded using high speed photography and fracture parameters for dynamically loaded stationary cracks are obtained. Measurements suggest significant crack initiation toughness reduction under dynamic loading conditions.