Relationship between tensile strength and porosity for foamed metals under equal speed biaxial tension

Abstract

A preliminary experimental investigation has been carried out on an isotropic three dimensional reticulated foamed metal with high porosity under biaxial tensile loading. The approximate relationship between tensile strength of these materials and their porosity has been evaluated under equal-speed biaxial tension loading. The mathematical formula is proved to be in a good agreement with the experimental data for nickel foam.     

A new analytical method for stress intensity factors based on insitu measurement of crack deformation under biaxial tension

A new approach for the calculation of stress intensity factors (SIF) for isotropic and orthotropic materials under biaxial tension loading was proposed in this paper. In order to determine SIF from the full-field displacement data, an asymptotic expansion of the crack tip displacement field was performed. The deforming shape and surface residual stress of the crack tip was obtained at the early extended stage of the loading process by using optical microscope and X-ray diffraction measurement. During this stage, a modified Dugdale Model, which takes into account the coupled effect at the crack tip, was proposed for the open displacement of the crack tip. In this paper, the SIFs of two types of silicon steel sheet with isotropic and orthotropic properties were calculated using the modified Dugdale Model based on the biaxial tension experimental data. From the results, it was found that analysis using the modified Dugdale Model is an effective way to evaluate SIF under biaxial stress.     

On the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loading

In this paper, the modified Wöhler curve method proposed by Susmel and Lazzarin is employed to predict the fatigue life of welded connections subjected to biaxial cyclic loading. This criterion is reformulated here in order not to take into account the mean stress effect, as suggested by several design codes (at least when welded connections are not completely stress relieved). The accuracy of the proposed method in fatigue lifetime estimation was evaluated by using a number of data sets taken from the literature. The modified Wöhler curve method was applied in terms of nominal stresses and was calibrated using the uniaxial and torsional fatigue curve determined by reanalysing the experimental data, as well as using the standard fatigue curves of the Eurocode 3. The proposed approach was seen to be successful, giving multiaxial fatigue life predictions located within the widest scatter band related either to uniaxial or to torsional data, independently of both out‐of‐phase angle and load ratio value. Finally, the accuracy of the modified Wöhler curve method was compared to the one obtained by applying the procedure suggested by the Eurocode 3: the proposed criterion is demonstrated to be much more accurate and reliable than the standard one.     

A continuum elastic–plastic model for woven-fabric/polymer-matrix composite materials under biaxial stresses

In this study a simple continuum model for the macro-mechanical prediction of the elastic–plastic behavior of woven-fabric/polymer-matrix composites has been proposed. This model uses a scalar hardening parameter (which is a function of the current applied stress state) instead of an effective stress-strain relation to determine plastic strain increments. For simplicity, the stresses are expressed as invariants based on the material symmetry. It has been shown, by the use of experimental data for two different woven-fabric/polymer-matrix composite materials, that the newly proposed model accurately describes the non-linear mechanical behavior for different in-plane biaxial stress states ranging from pure shear to pure tension.     

复合材料双面贴补修理拉伸解析分析模型及试验验证

复合材料胶接修理是一种有效并且低成本的修理技术。本文建立了复合材料层合板双面贴补胶接修理解析分析模型。模型中考虑了搭接区阶梯末端截面积变化细节。预测失效时,层合板采用最大应变准则,胶层采用最大剪应变准则和损伤区域理论。定义了残差函数来表征极限载荷解析计算结果与试验值的接近程度。通过试验对解析模型得到的等效刚度与极限载荷进行了验证。解析分析结果与试验数据对比表明:复合材料层合板双面贴补等效刚度随着搭接长度的增加单调增加。解析模型计算的等效刚度与试验结果最大误差不超过15%。当损伤特征长度为4%时,损伤区域理论对应极限载荷残差值最小,仅为4.30%,最大剪应变准则预测极限载荷的残差值为6.41%。解析模型分析表明,双面贴补极限载荷随着搭接长度的增加表现为快速增长、缓慢增长和几乎不增长三个阶段。搭接长度结合结构减重等限制因素应选择15~35mm为宜。     

A new path‐dependent multiaxial fatigue model for metals under different paths

Based on the critical plane approach, a new path‐dependent multiaxial fatigue model in low‐cycle fatigue is proposed. The proposed model includes damage contribution from four sources: the normal strain amplitude, the shear strain amplitude on the critical plane, the hydrostatic mean strain and a new path‐dependent factor. The effect of mean strain is considered by the hydrostatic mean strain. The experimental data of 11 kinds of materials are used to demonstrate the effectiveness of this new model under both zero and non‐zero mean strain multiaxial loading path.     

Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: A numerical and experimental analysis

In the present work the influence at micromechanical scale of thermal residual stresses, originated in the cooling down associated to the curing process of fibrous composites, on inter-fibre failure under transverse tension is studied. In particular, the effect of the presence of thermal residual stresses on the appearance of the first debonds is discussed analytically, whereas later steps of the mechanism of damage, i.e. the growth of interface cracks and their kinking towards the matrix, are analysed by means of a single fibre model and making use of the Boundary Element Method (BEM). The results are evaluated applying Interfacial Fracture Mechanics concepts. The conclusions obtained predict, at least in the case of dilute fibre packing, a protective effect of thermal residual stresses against failure initiation, the morphology of the damage not being significantly affected in comparison with the case in which these stresses are not considered. Experimental tests are carried out, the results agreeing with the conclusions of the numerical analysis.     

A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings

Based on the critical plane approach, a new damage parameter for multiaxial fatigue damage is presented. Both components of strain and stress are considered in this parameter. Thus, a new multiaxial fatigue damage model is given based on the critical plane approach. The capability of fatigue life prediction for the proposed fatigue damage model is checked against the experimental data of Hot-rolled 45 Steel, S460N Steel, 1045HR Steel, 30CrMnSiNi2A alloy steel, and GH4169 alloy at elevated temperature, and the predicted results are compared with results from common multiaxial fatigue model. It is demonstrated that the proposed criterion gives better satisfactory results for all the five checked materials.     

A structural constitutive model for chemically treated planar tissues under biaxial loading

Chemically treated, biologically derived soft collagenous tissues are used extensively in medical devices. To enable prosthesis design through computational methods, physically realistic constitutive models are required. In the present study, a structural approach was utilized that incorporated experimentally measured angular distribution of collagen fibers. Using biaxial mechanical data from our previous study (Annals of Biomedical Engineering, vol. 26(5), pp. 892–902, 1998), the effective fiber and matrix stress–strain responses were predicted. The agreement with the experimental data supported the assumption that the mechanical effects of chemical treatment are equivalent to the addition of an isotropic elastic matrix. An important utility of this model is its ability to separate the effects of chemical treatment on the fibers and matrix. Applications of this approach include utilization in the design of novel chemical treatments that produce specific mechanical responses, the study of fatigue damage, and finite element implementation for tissue engineering scaffold design. Received 4 November 1999     

Phenomenological rheological model and the criterion of failure of metals under uniaxial stress

The article suggests an energy alternative of the phenomenological rheological equations and criteria of failure of metals for a broad range of stresses including stresses higher than yield stress. The approach is based on the hypothesis that the damage to material is proportional to the linear combination of the work of true stress on creep strain and plastic strain. From the same positions the article describes the nonmonotonic nature of the curve of elastoplastic strain, the nonlinear nature of the curve of creep limit, it identifies the stage of avalanche creep, etc. The model was experimentally checked on the alloy ÉP742 at 650 and 750°C. Agreement between theoretical and experimental data was obtained.Translated from Problemy Prochnosti, No. 11, pp. 13–19, November, 1991.     

Yield and failure envelope for ice under multiaxial compressive stresses

An analysis has been made on Jones' (1982) experimental results on the yield strength of ice. The available data were obtained from triaxial tests performed on polycrystalline isotropic ice. Maximum confining pressure reached 85 MPa. These data have been analysed in order to formulate a proper yield criterion for ice (Nadreau, 1985). The model was influenced by previous studies on ice yield criteria which were derived from equations used in the field of rock and soil mechanics. One of the main advantages of this new formulation is its ability to consider the hydrostatic pressure at which ice changes to water (Mellor, 1980). The yield surface is a cubic function of the invariants of the stress tensors. The parameters involved in the definition of the yield envelope are functions of the hydrostatic pressure at phase change and of the strain rate applied to the sample. The three-dimensional surface defined by this criterion is teardrop-shaped and symmetrical around the hydrostatic line. The volume of this teardrop envelope is found to increase as a function of increasing strain-rate.     

Analysis of brittle fracture under the combined stresses of tension and compression

Brittle fractures occurring under biaxial stress states were analysed based on the weakest link model using the mixed mode fracture criterion. Expressions for the mixed mode fracture criterion were chosen for application to the negativeK _l region, corresponding to the compressive stress for the crack. Calculations for biaxial strength with randomly oriented constant-length cracks from the mixed mode fracture criterion were made in the region ofK _I>0 because an unstable fracture seems to occur in this region. The results indicated that the tensile stress component in the combined tension and compression stress state remains constant when the compressive component is smaller than the critical value, which is given by [1 –(K _c/K _c)²]_t derived from the mixed mode fracture criterion, (K /K _c) + (K /K _c)² = 1. Considering the statistical effects, however, calculation of the biaxial strength is modified to result in: (1) lowering the biaxial tensile strength, and in (2) a smooth transition from the constant tensile strength region to the decreasing strength region under the combined tension and compression stress. This suggests that the highK _IIc/K_Ic ratio results in the increase in the compressive strength relative to the tensile strength.     

A new plasticity and failure model for ballistic application

Ballistic phenomena give rise to a plethora of failure modes that compete. Johnson–Cook (JC) plasticity and failure models have been extremely successful because, while being conceptually simple, they capture the essence of the operative mechanics and they provide reasonably good predictions for ballistic limits. Nevertheless, the Johnson–Cook models, due to their isotropic flow and failure surface, cannot reproduce certain failure modes commonly seen in quasistatic tests: cup and cone failure, slanted failure in tensile specimens, and slanted failure in compression specimens. This work shows that by introducing the third invariant (or Lode angle) in both the JC plasticity and damage models, cup and cone, and slanted failure modes arise naturally. After the model is presented it is exercised with a material taken from the literature to predict successfully Taylor anvil and ballistic penetration failure patterns.     

A new variant for measuring the surface tension of liquid metals and alloys by the oscillating drop method

The theoretical background of the oscillating drop technique for measuring surface tension is briefly presented and the different analysis procedures are cited. A new method is described for obtaining oscillation frequencies by fast fourier transformation (FFT) of the pyrometer voltage signals from temperature measurements at the top of the levitated sample. The results on the first experiments on liquid nickel are in a good agreement with the hterature data.Paper presented at the Fourth International Workshop on Subsecond Thermophysics. June 27–29, 1995, Köln, Germany.     

A new failure criterion for the Gurson-Tvergaard dilational constitutive model

In the Gurson-Tvergaard model a failure criterion has to be used to signify the void coalescence. In the literature, a constant critical void volume fraction criterion has been widely used. However, it is questionable whether the critical void volume fraction is a material constant and, furthermore, it is also difficult in practice to determine the constant. By modifying Thomason's plastic limit-load model, a new failure criterion which is fully compatible with the Gurson-Tvergaard model, is presented in this study. In the present criterion, the void coalescence failure mechanism by internal necking has been considered and the material failure is a natural result of the development of dual constitutive, stable and unstable, responses. In practical application of the present criterion, no critical void volume fraction needs to be pre-determined either numerically or experimentally. Furthermore, according to the new criterion, the void volume fraction corresponding to void coalescence is not a material constant, rather a function of stress triaxiality. The predictions using the present criterion have been compared with the finite element results by Koplik and Needleman, and very good agreement is observed. The potential advantage of this criterion and other related issues are discussed.     

A model for foamed cementing of oil and gas wells

We present a two-dimensional model of the primary cementing process for foamed cement slurries. Foamed cement slurries have a number of claimed advantages, but also have a pressure-dependent density and rheology. The rheology is hard to quantify fully over all ranges of foam quality, which compromises the accuracy of models. The density variation is due to expansion/compression of the gas phase along the well, caused by variations in the static pressure. We show that in the absence of careful control, buoyancy-driven instabilities can result in the annulus, as the foamed slurry expands and the density drops below that of the displaced drilling mud. These instabilities appear to be of a classic porous media/Hele-Shaw cell fingering type, triggered by a threshold unstable density difference. We show that these instabilities are amplified by wellbore eccentricity, occurring lower in the well than in a concentric annulus. Our results question the safe usage of foamed cements in primary cementing.