Jwo Pan

Plane-stress crack-tip fields for pressure-sensitive dilatant materials

Abstract In this paper we present plane-stress crack-tip stress and strain fields for pressure-sensitive dilatant materials. A hydrostatic stress-dependent yield criterion and the normality flow rule are used to account for pressure-sensitive yielding and plastic dilatancy. The material hardening response is specified by a power-law relation. The plane-stress mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, J. Mech. Phys. Solids 16 , 13–31 and 337–347, 1968; Rice and Rosengren, J. Mech. Phys. Solids 16 , 1–12, 1968). The angular variations of the fields depend on the material hardening exponent and the pressure sensitivity parameter. Our low-hardening solutions for different degrees of pressure sensitivity agree well with the corresponding perfectly plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on crack-tip fields is the lowering of the opening stress and the hydrostatic stress directly ahead of the crack tip. This effect, similar to that under plane-strain conditions (Li and Pan, to appear in J. Appl. Mech . 1989), has implications in the material toughening observed in some ceramic and polymeric composites.

PLANE-STRESS MIXED-MODE NEAR-TIP FIELDS IN ELASTIC PERFECTLY PLASTIC SOLIDS

Within the context of the small-strain approach, the plane-stress mixed-mode near-tip fields of a stationary crack in an elastic perfectly plastic solid under small-scale yielding conditions are examined by finite element methods. The finite element results show that asymptotically at the crack tip two elastic sectors exist under near mode I mixed-mode loading conditions, and one elastic sector exists under near mode II mixed-mode loading conditions. The fully yielded near-tip field, plastically deformed at all angles, is obtained only under pure mode II loading conditions. The corresponding asymptotic crack-tip solutions (consisting of constant stress sectors, curved fan sectors, and elastic sectors) are also constructed. The asymptotic crack-tip stress solutions agree well with the finite element results for the complete range of mixed-mode loadings. Some similarities and differences between the near-tip fields under plane-stress and plane-strain conditions are also discussed. A SUBSTANTIAL understanding of the near-tip structures for power-law hardening materials obeying a deformation plasticity theory has been achieved in recent years. Representative works along this line are those of Hutchinson( 1,2), Rice(3), and Rice and Rosengren(4) for a crack under pure mode I and pure mode II loading conditions, and of Shih(S, 61 under mixed-mode loading conditions. For power-law hardening materials, the asymptotic crack-tip stress and strain fields possess the well-known HRR singularity. The corresponding crack-tip field solutions for perfectly plastic materials were also proposed by the above authors, with the assumption that the material surrounding the crack-tip is fully yielded at all angles. These solutions agree with the perfectly plastic limits of the corresponding asymptotic solutions for power-law hardening materials, and contain radial stress discontinuities under plane-strain near mode I mixed-mode conditions and under plane-stress mode I and mixed-mode conditions (for anisotropic perfectly plastic materials, see Pan(7,8)). Within the framework of rigid perfectly plastic theory (where the elastic strain is neglected), a line of discontinuity in the stress field may be viewed as a mathematical idealization of an infinitively thin elastic region separating two plastic regions. However, for perfectly plastic materials when the material elasticity is considered, it seems reasonable to ask: how does the elastic strain affect the near-tip field structures? To address the above issue under plane-strain conditions, Gao(9) proposed the crack-tip stress fields that contain two elastic sectors under mixed-mode loading conditions. However, the finite element computations carried out by Saka et aL(lO) showed that only one elastic sector exists around the crack tip under mixed-mode loading and small-scale yielding conditions, with Poissons ratio being nearly l/2. A systematic investigation of the plane-strain mixed-mode crack-tip fields has been conducted by Dong and Pan(l 1, 121. Their computational results and asymptotic analysis show that, as the limiting steady-stress state near the crack tip, the near mode I crack-tip fields do contain an elastic sector, but they differ from the crack-tip fields proposed by Saka et aL(lO) by a constant stress sector separating the elastic sector and a neighboring fan sector. The corresponding conditions for the existence of the elastic sector were examined by asymptotic analyses and verified by finite element computations. Very little information is available in the literature pertaining to the above issues for elastic perfectly plastic materials, particularly under plane-stress mixed-mode loading conditions, despite its practical importance to structural problems. To our best knowledge, a detailed finite

Effects of elasticity and pressure-sensitive yielding on plane-stress crack-tip fields

The asymptotic plane-stress mode 1 crack-tip fields under small-scale yielding for pressure- sensitive materials are investigated. The yield criterion for these materials is described by a linear combination of the effective stress and the hydrostatic stress. Plastic dilatancy is introduced by normality flow rule. A closed-form genera1 asymptotic solution for singular centered fan sectors is given as a function of p, which is a pressure sensitivity parameter introduced in the yield condition. When elastic-perfectly plastic behavior is considered, the finite element results show the existence of elastic sectors bordering the stress-free crack faces. The near-tip stresses of the finite element results agree well with those of the corresponding asymptotic analysis. The angular spans of the elastic and plastic sectors vary with the value of p. The parameter p also has significant effects on the sizes and shapes of the plastic zones. The contribution of hydrostatic stress in the yield criterion for this class of pressure-sensitive materials extends the boundary of the plastic zone much farther in front of the crack-tip than that for incompressible Mises materials.

Computational models for simulations of lithium-ion battery modules under quasi-static and dynamic constrained compression tests

ABSTRACT A computational model is developed for simulations of representative volume element (RVE) specimens of lithium-ion battery modules under in-plane constrained compression tests. The model is based on the mechanical properties of the heat dissipater, the foam and the macro behaviour of the cell under quasi-static loading conditions. The semi-homogenised computational model allows for computational efficiency with sacrifice of the detailed buckling behaviour of the battery cell components. The results from the model under quasi-static and dynamic loading conditions are compared to those from experiments. The nominal stress-strain responses of the specimen and the deformation patterns of the heat dissipater obtained from the computational results compare fairly well with the experimental results. Both experimental and computational results show that for the given dynamic displacement rates the nominal stress at which the heat dissipater begins to buckle under dynamic loading conditions is about twice as high as that under quasi-static loading conditions and that the nominal stresses at large nominal strains under dynamic loading conditions are slightly higher than those under quasi-static loading conditions. The results of this investigation suggest that when a less detailed model is used for simulations under crash conditions, the higher initial buckling stresses should be considered.

Microstructures and Failure Mechanisms of Spot Friction Welds in Lap-Shear Specimens of Aluminum 5754 Sheets

Microstructures and failure mechanisms of spot friction welds (SFW) in aluminum 5754 lap-shear specimens were investigated. In order to study the effect of tool geometry on the joint strength of spot friction welds, a concave tool and a flat tool were used. In order to understand the effect of tool penetration depth on the joint strength, spot friction welds were prepared with two different penetration depths for each tool. The results indicated that the concave tool produced slightly higher joint strength than the flat tool. The joint strength did not change for the two depths for the flat tool whereas the joint strength slightly increases as the penetration depth increases for the concave tool. The experimental results show that the failure mechanism is necking and shearing for the spot friction welds made by both tools. The failure was initiated and fractured through the upper sheet under the shoulder indentation near the crack tip.

Hold-Time Effect on Thermo-Mechanical Fatigue Life and its Implications in Durability Analysis of Components and Systems

Thermo-mechanical fatigue (TMF) resistance of engineering materials is extremely important for the durability and reliability of components and systems subjected to combined thermal and mechanical loadings. However, TMF testing, modeling, simulation, validation, and the subsequent implementation of the findings into product design are challenging tasks because of the difficulties not only in testing but also in results interpretation and in the identification of the deformation and failure mechanisms. Under combined high-temperature and severe mechanical loading conditions, creep and oxidation mechanisms are activated and time-dependent failure mechanisms are superimposed to cycle-dependent fatigue, making the life assessment very complex. In this paper, the testing procedures and results for high-temperature fatigue testing using flat specimens and thermal-fatigue testing using V-shape specimens are reported; emphasis is given to hold-time effects and the possible underlying mechanisms. The uncertainty nature and the probabilistic characteristics of the V-shape specimen test data are also presented. Finally, the impact of hold-time effect on current product design and validation procedure is discussed in terms of virtual life assessment.

Failure Mode and Fatigue Behavior of Dissimilar Friction Stir Spot Welds in Lap-Shear Specimens of Transformation-Induced Plasticity Steel and Hot-Stamped Boron Steel Sheets

Failure mode and fatigue behavior of dissimilar friction stir spot welds in lap-shear specimens of transformation-induced plasticity steel (TRIP780) and hot-stamped boron steel (HSBS) sheets are examined in this paper. Optical micrographs of the dissimilar TRIP780/HSBS friction stir spot welds made by a concave silicon nitride tool before and after testing are obtained and examined. These micrographs indicate that subject to quasi-static and cyclic loading conditions, the TRIP780/HSBS welds fail from cracks growing through the TRIP780 sheets where the tool was plunged into and the thickness was reduced. The bending moments and the transverse shear force near the welds are derived with consideration of the load offset, the weld gap, and the bend distance for calculation of analytical global stress intensity factor solutions for the welds in lap-shear specimens. A fatigue model of kinked crack growth is used to estimate fatigue lives based on the local stress intensity factor solutions for kinked cracks. The estimated fatigue lives with consideration of the weld gap and the bend distance are in agreement with the fatigue test results under low-cycle loading conditions and lower than the fatigue test results under high-cycle loading conditions. The estimated fatigue lives suggest that the weld gap and the bend distance can significantly affect fatigue lives of the friction stir spot welds in lap-shear specimens under cyclic loading conditions.

Failure mechanism of laser welds in lap-shear specimens of a high strength low alloy steel

In this study, the failure mechanism of laser welds in lap-shear specimens of a high strength low alloy (HSLA) steel under quasi-static loading conditions is examined based on the experimental results. Optical micrographs of the welds in specimens before tests were examined to understand the microstructure near the weld. A micrographic analysis of the failed welds in lap-shear specimens indicates a ductile necking/shear failure mechanism near the heat affected zone. Micro-hardness tests were conducted to provide an assessment of the mechanical properties of the joint area which has varying microstructure due to the welding process. A finite element analysis was also carried out to identify the effects of the weld geometry and different mechanical properties of the weld and heat affected zones on the failure mechanism. The computational results of the finite element analysis indicate that the material inhomogeneity and geometry of the weld bead play an important role in the ductile necking/shear failure mechanism. The computational results match well with the experimental observations of the necking/shear failure and its location. A finite element analysis with consideration of void nucleation and growth based on the Gurson yield function was also carried out. The results of the finite element analysis based on the Gurson yield function are in good agreement with the experimental observations of the initiation of ductile fracture and its location.Copyright

Crack Tip Strain Distributions and Their Implications to Crack Growth Rate due to Stress Corrosion Cracking

In this paper, stress and strain distributions near a crack tip in a round compact tension specimen of elastic-plastic materials are obtained by finite element analyses. The strain distributions are used to explore the use of the crack tip strain distributions for crack growth rate models due to stress corrosion cracking in unirradiated and irradiated steels with different yield stresses and hardening behaviors. Both power-law hardening and perfectly plastic materials are considered. The computational results indicate that the critical radial distance to the tip based on the crack tip opening displacement is outside of the Hutchinson-Rice-Rosengren (HRR) dominant zone for power-law hardening materials in a round compact tension specimen under the stress intensity factor typically considered for stress corrosion cracking. For both the power-law hardening and perfectly plastic materials, the computational results show that the strain distributions are different from those of the analytical solutions for the range of the radial distance larger than the critical radial distance based on the crack opening displacement within the plastic zones. The computational results suggest that for the stress intensity factor typically considered for stress corrosion crack growth rate models, computational results are needed to estimate the strain rate for developing crack growth rate models to correlate to the experimental data.Copyright

Effects of weld geometry on stress intensity factor solutions for laser welds in lap-shear specimens

In this paper, the effects of weld geometry on the stress intensity factor solutions for laser welds in lap-shear specimens are investigated. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for use with the stress intensity factor solutions for kinked cracks to correlate and estimate fatigue lives of laser welded lap-shear specimens. The effects of the weld protrusion on the stress intensity factor solutions for the pre-existing cracks in lap-shear specimens are also investigated. The presence of the weld protrusion decreases the stress intensity factor solutions for the pre-existing crack near the weld protrusion for the load carrying sheets and the lower stress intensity factor solutions can be used to explain more favorable conditions for kinked fatigue crack propagation from the other pre-existing crack tip and to estimate fatigue lives of laser welded lap-shear specimens under high cycle loading conditions as observed in experiments.© 2011 ASME