ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS

The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the U-transformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.

Evaluation of stress intensity factors of thin AZ31B magnesium alloy plate under biaxial tensile loading

Stress intensity factors of thin AZ31B magnesium alloy sheet under biaxial tension loading were analyzed by modified Dugdale model. K-values with crack angle of 90° obviously show that there is no influence of the loading condition in Mode-I. In the 45° case, K1 values are obtained within 10% errors when they are calculated by modified Dugdale model under biaxial loading. It is concluded that the modified Dugdale model is one of effective ways to evaluate stress intensity factor of AZ31 magnesium alloy sheet appropriately.

A Rate-Dependent Crystal Plasticity Analysis of Orientation Stability in Biaxial Tension of Magnesium

The development of texture during plastic deformation plays an important role in determining the stretch formability of magnesium alloy sheets.In this study,the orientation stability during equibiaxial tension of magnesium was analyzed based on three dimensional lattice rotations calculated by using a rate-dependent crystal plasticity model and assuming five different combinations of slip modes.The results show that no orientations can satisfy the stability criteria with both zero rotation velocity and convergent orientation flow in all dimensions.However,relatively stable orientations with zero rotation velocity and an overall convergence are found.They are featured by characteristic alignments of specific crystallographic directions in the macroscopic axis of contraction,depending on the slip modes involved in the deformation.It is also shown that the orientation stability varies significantly with the deviation of deformation mode from equibiaxial tension.The simulation results are briefly discussed in comparison with pre-existing experiments.

On the modeling of deformation mechanisms in a Mg-3Al-1Zn alloy under biaxial tension

Although the{10-12}twinning behavior of Mg alloys under uniaxial tension and compression has been extensively investigated,the simulations of{10-12}twinning behavior under biaxial tension have rarely been reported.In this work,the EVPSC-TDT model is first employed to systematically investigate the deformation behavior of a Mg alloy AZ31 plate under biaxial tension in the RD-TD and ND-TD planes.The RD,TD and ND refer to the rolling direction,transverse direction,and normal direction of the hot rolled plate.The measured stress-strain curves and texture evolutions are well predicted and the con-tours of plastic work under biaxial tension are also constructed for comparison with experiments.The plastic response has been interpreted in terms of relative activities of various deformation modes.For bi-axial tension in the RD-TD plane,basal and pyramidal slips mainly contribute to the plastic deformation for stress ratios ofσRD:σTD=1:2 to 2:1.Prismatic slip becomes more active forσRD:σTD=1:4 and 4:1.Compression twinning could be activated and so cause texture reorientation at large strains,especially forσRD:σTD=1:1.The six-fold feature of{10-10}pole figure could still be observed forσRD:σTD=1:4 and 4:1 at large strain.For biaxial tension in the ND-TD plane,tensile twinning plays an important role forσND:σTD≥1:2,while prismatic slip contributes to plastic deformation for the other cases.With the in-crease of stress ratio fromσND:σTD≥1:1 to 1:0,the predicted twin volume fractions(VFs)at a specific strain along the ND,εND,almost linearly decrease,however,it is seen that the experimental ones at given strains along the ND do not follow such a trend with the measured twin VFs within the range of stress ratios,2:1≤σND:σTD≤6:1,clearly being overestimated,and the difference between experiments and simulations becomes most obvious at the relatively small strain ofεND=0.015.The possible reasons for the observed difference are discussed.

Fracture behaviors of commercially pure titanium under biaxial tension:Experiment and modeling

The fracture behaviors and associated mechanisms of metallic materials under biaxial stress are vital for their manufacturability and service performance.In this work,the fracture behaviors of commercially pure titanium(CP-Ti)under quasi-uniaxial and equi-biaxial tension were investigated by using the digital image correlation technique and finite element modeling.The fracture behaviors under quasi-uniaxial tension were characterized by a general normal fracture.In contrast,normal fracture firstly occurred per-pendicular to the rolling direction(RD)under equi-biaxial tension,followed by secondary shear fracture along the 45°direction relative to the RD.The normal fracture was attributed to the lower strain hard-ening ability in RD compared to the transverse direction(TD)induced by the TD-split type basal texture.The different hardening abilities introduced large shear stress in the 45°direction,which contributed sig-nificantly to the secondary shear fracture.An anisotropy parameter K(△S_(s)/σ_(s)),defined as the ratio of the equivalent effective traction stress to the yield strength,was proposed for the first time,to predict the fracture path with the impact of crystallographic preferred orientation.