Stress analysis of borehole subjected to fluid injection in transversely isotropic poroelastic medium

This paper proposes an analytical solution, using the combined Laplace–Fourier integral transform technique, for a borehole drilled in transversely isotropic porous medium and subjected to a fluid discharge over a finite length of its surface. Especially, the coupled boundary condition between the total radial stress and injection-induced pore pressure at the borehole surface is addressed in a rigorous fashion, which leads essentially to a set of dual integral equations that can be solved through standard numerical procedure. The study focuses on the calculation of stress fields around the borehole with particular attention given to the time-dependent effective tangential stress and pore pressure distributions. Numerical solutions are presented for verification with those recently derived for the limiting case of an isotropic medium and, more importantly, to investigate the influences of material anisotropy on the stress responses of the borehole and porous medium.     

A combined necking and shear localization analysis for aluminum sheets under biaxial stretching conditions

A combined necking and shear localization analysis is adopted to model the failures of two aluminum sheets, AA5754 and AA6111, under biaxial stretching conditions. The approach is based on the assumption that the reduction of thickness or the necking mode is modeled by a plane stress formulation and the final failure mode of shear localization is modeled by a generalized plane strain formulation. The sheet material is modeled by an elastic-viscoplastic constitutive relation that accounts for the potential surface curvature, material plastic anisotropy, material rate sensitivity, and the softening due to the nucleation, growth, and coalescence of microvoids. Specifically, the necking/shear failure of the aluminum sheets is modeled under uniaxial tension, plane strain tension and equal biaxial tension. The results based on the mechanics model presented in this paper are in agreement with those based on the forming limit diagrams (FLDs) and tensile tests. When the necking mode is suppressed, the failure strains are also determined under plane strain conditions. These failure strains can be used as guidances for estimation of the surface failure strains on the stretching sides of the aluminum sheets under plane strain bending conditions. The estimated surface failure strains are higher than the failure strains of the forming limit diagrams under plane strain stretching conditions. The results are consistent with experimental observations where the surface failure strains of the aluminum sheets increase significantly on the stretching sides of the sheets under bending conditions. The results also indicate that when a considerable amount of necking is observed for a sheet metal under stretching conditions, the surface failure strains on the stretching sides of the sheet metal under bending conditions can be significantly higher.     

页岩层理方位及强度对水力压裂的影响

为了研究页岩天然层理倾角及强度等对水力压裂裂纹扩展的影响,采用室内水力压裂实验,通过监测孔直接对裂纹扩展的实时监测和注水压力信息及试件压裂后的剖切,分析层理倾角、强度等对压裂裂纹扩展的影响。实验结果表明:水力压裂过程中,垂直最小地应力稳定扩展的主裂缝遇层理时,层理面与主裂缝初始扩展方向夹角越小,主裂缝越易沿着层理面方向扩展,层理面与主裂缝初始扩展方向夹角越大,主裂缝遇层理面时越易贯穿层理面沿原方向扩展;层理方位,地应力及基质抗拉强度不变,层理的抗拉强度远弱于基质抗拉强度时,主裂缝与层理面相遇后越易沿着层理面方向扩展,层理抗拉强度与基质抗拉强度越相近,主裂缝遇层理时越易贯穿层理沿原方向扩展;层理方位和强度不变,地应力及应力差越大,主裂缝遇层理后越易贯穿层理面沿原方向扩展。     

理想正交各向异性弹塑性材料平面应力条件下Ⅰ型静止裂纹尖端场

在本文中,以 Hill 的塑性理论为基础,详细地讨论了理想正交各向异性弹塑性材料,平面应力条件下Ⅰ型静止裂纹尖端场解。裂纹尖端应力场不包含应力间断线,但包含弹性区。分析的结果表明(i)对于平面应力静止裂纹问题,应力场解不是唯一的,场解中的自由参数必须由远场条件来确定。(ii)裂纹尖端的应力、应变的奇异性,无论是各向异性材料还是各向同性材料,都是相同的。但在各向异性材料中,各向异性参数影响着应力、应变的幅度和分布。     

Propagation of thin plastic zones in the vicinity of a normally separating crack

A problem of the development of a plastic zone in the vicinity of a physical cut in the plain strain and stress states is posed and solved on the basis of a discrete deformation model under the assumption of an ideal elastoplastic medium. The Tresca yield condition and the ultimate plasticity condition are used in studying the plane stress state. The dependence of the plastic zone length on the external load is compared with a similar dependence obtained on the basis of the Leonov-Panasyuk-Dugdale model. In contrast to the Leonov-Panasyuk-Dugdale model, the distributions of stresses and lengths of plastic zones in the plane strain and stress states are found to be substantially different if elastic compressibility and compressive-tensile stresses along the cut direction are taken into account.     

On non-associative anisotropic finite plasticity fully coupled with isotropic ductile damage for metal forming

In this work, non-associative finite strain anisotropic elastoplasticity fully coupled with ductile damage is considered using a thermodynamically consistent framework. First, the kinematics of large strain based on multiplicative decomposition of the total transformation gradient using the rotating frame formulation, is recalled and different objective derivatives defined. By using different anisotropic equivalent stresses (quadratic and non-quadratic) in yield function and in plastic potential, the evolution equations for all the dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. The effect of the objective derivatives and the equivalent stresses (quadratic or non-quadratic) on the plastic flow anisotropy and the hardening evolution with damage is considered. Numerical aspects mainly related to the time integration of the fully coupled constitutive equations are discussed. Applications are made to the AISI 304 sheet metal by considering different loading paths as tensile, shear, plane tensile and bulge tests. For each loading path the effect of the rotating frame, the equivalent stress (quadratic or non-quadratic) and the normality rule (with respect to yield function or to the plastic potential) are discussed on the light of some available experimental results.     

Modelling inelastic behaviour of orthotropic metals in a unique alignment of deviatoric plane within the stress space

A finite strain constitutive model to predict the deformation behaviour of orthotropic metals is developed in this paper. The important features of this constitutive model are the multiplicative decomposition of the deformation gradient and a new Mandel stress tensor combined with the new stress tensor decomposition generalized into deviatoric and spherical parts. The elastic free energy function and the yield function are defined within an invariant theory by means of the structural tensors. The Hill’s yield criterion is adopted to characterize plastic orthotropy, and the thermally micromechanical-based model, Mechanical Threshold Model (MTS) is used as a referential curve to control the yield surface expansion using an isotropic plastic hardening assumption. The model complexity is further extended by coupling the formulation with the shock equation of state (EOS). The proposed formulation is integrated in the isoclinic configuration and allows for a unique treatment for elastic and plastic anisotropy. The effects of elastic anisotropy are taken into account through the stress tensor decomposition and plastic anisotropy through yield surface defined in the generalized deviatoric plane perpendicular to the generalized pressure. The proposed formulation of this work is implemented into the Lawrence Livermore National Laboratory-DYNA3D code by the modification of several subroutines in the code. The capability of the new constitutive model to capture strain rate and temperature sensitivity is then validated. The final part of this process is a comparison of the results generated by the proposed constitutive model against the available experimental data from both the Plate Impact test and Taylor Cylinder Impact test. A good agreement between experimental and simulation is obtained in each test.     

The bending moment and springback in pure bending of anisotropic sheets

Finite deformation rigid plastic and elastic–plastic analyses of plane strain pure bending of a plastically anisotropic sheet is presented. An efficient method for finding the exact solution is proposed by extending the previously developed method to the stage of unloading. Using this method the solutions are obtained in closed form or reduced to a numerical treatment of ordinary integrals, or an ordinary differential equation, or transcendental equations. An effect of plastic anisotropy and elastic properties on the bending moment is analyzed. The distribution of residual stresses is illustrated and an effect of material and process parameters on springback is investigated.     

Effect of phase interactions on crystal stress evolution over crystal orientation space under elastoplastic deformation of two-phase polycrystalline solids

It has been known for decades that crystal stress directions move toward the vertices of the single crystal yield surface (SCYS) during plastic flow of polycrystalline solids to satisfy the deformation compatibility among crystals. The alignment of crystal stress with a SCYS vertex is affected not only by plastic anisotropy, but also by other factors such as elastic anisotropy, loading direction, and grain interactions. Among the factors contributing to the degree of alignment, the effect of phase interactions on the crystal stress evolution during plastic flow has not been extensively investigated. In this research, the effect of phase interactions on the crystal stress direction evolution is investigated using simulations of an elastoplastically deforming two-phase (Cu/Fe) polycrystalline solid calibrated to a neutron diffraction experiment. By mapping the simulated crystal stresses over the crystal orientation space, crystal-orientation-dependent nonuniform partitioning of the crystal stress between phases can be observed. An analysis of the distribution of angles between the SCYS vertex and the crystal stress based on the simulation of the two-phase material shows that the crystal stress evolution pattern during plastic flow is strongly affected by phase interactions. These interactions result in low alignment and greater dispersion angles between the crystal stresses and SCYS vertices, particularly in the strong phase.     

Finite strain analysis of simple shear using recent anisotropic yield criteria

The finite strain response of a rectangular block subjected to constrained simple shearing deformations is considered in order to evaluate the predictive capability of some recently proposed anisotropic yield functions. It is shown that, in the presence of plane anisotropy, the prediction of realistic second order normal stresses cannot be expected since every different initial orientation of the material axes relative to the loading axes results in a different response due to the rotation of the material axes with shear. Parametric studies are performed in order to determine possible limits on the material constants so that the predicted normal stresses remain second order with respect to the shear stress itself. Our numerical results indicate that, in particular, the commonly employed range of one parameter associated with grain related anisotropy renders results which no longer imply predicting a proper second order effect but rather introduces errors of the first order. The results suggest that the modelling of anisotropy with such phenomenological anisotropic yield functions should be limited to near-quadratic yield surfaces for applications involving stress states outside the biaxial tensile stress range.     

Nucleation of micro-cracks for polycrystalline metal with anisotropy: micro-stress evaluation

Presented is the local stresses on the crystallographic plane as they are influenced by the metal fracture with anisotropy. It is based on the nucleation of micro-cracks and its unstable equilibrium in a polycrystal with texture. Crystallographic texture causes non-uniform distribution of the crack nucleus orientations owing to their preference to expand or open on certain crystallographic planes. This is the main cause of anisotropy of cleavage fracture stress of textured metal. “Oriented” micro-stresses in textured metal contribute to the anisotropic effect. In view of what has been said, accumulated plastic strains at fracture is analysed.     

A model for the through-thickness elastic–plastic behaviour of paper

An elastic–plastic material model for the out-of-plane mechanical behaviour of paper is presented. This model enables simulation the elastic–plastic behaviour under high compressive loads in the through-thickness direction (ZD). Paper does not exhibit a sharp transition from elastic to elastic–plastic behaviour. This makes it advantageous to define critical stress states based on failure stresses rather than yield stresses. Moreover, the failure stress in out-of-plane shear is strongly affected by previous plastic through-thickness compression. To cover these two features, a model based on the idea of a bounding surface that grows in size with plastic compression is proposed. Here, both the bounding and the yield surfaces are suggested as parabolas in stress space. While the bounding surface is open for compressive loads, the yield surface is bordered by the maximum applied through-thickness compression.     

Stress across an elastoplastic boundary of a mode I crack: parabolic to hyperbolic plasticity transition

In previous work, the stresses of a mode I elastic–plastic fracture mechanics problem were analytically continued across a prescribed elastoplastic boundary for plane stress loading conditions involving a linear elastic/perfectly plastic material obeying the Tresca yield condition. Immediately across the elastic-plastic boundary, a nonlinear parabolic partial differential equation governs the plastic stress field. The present solution deals with stresses extending beyond the parabolic region into the hyperbolic region of the plastic zone. This analytical solution is obtained through a tranformation of the original system of nonlinear partial differential equations into a linear system with constant coefficients. The solution, so obtained, is expressible in terms of elementary transcendental functions. It also exhibits a limiting line which passes through the crack tip. This feature of the solution suggests the formation of a plastic hinge in the material.     

Unit cell debonding analyses for arbitrary orientation of plastic anisotropy

Debonding of rigid inclusions embedded in the elastic–plastic aluminum alloy Al 2090-T3 is analyzed numerically using a unit cell model taking full account of finite strains. The cell is subjected to overall biaxial plane strain tension and periodical boundary conditions are applied to represent arbitrary orientations of plastic anisotropy. Plastic anisotropy is considered using two phenomenological anisotropic yield criteria, namely Hill [Proceedings of the Royal Society of London A 193 (1948) 281] and Barlat et al. [International Journal of Plasticity 7 (1991) 693]. For this material plastic anisotropy delays debonding compared to plastic isotropy except for the case of Hill’s yield function when the tensile directions coincided with the principal axes of anisotropy. For some inclinations of the principal axes of anisotropy relative to the tensile directions, the stress strain responses are identical but the deformation modes are mirror images of each other.     

The effect of plastic anisotropy on compressive instability in sheet metal forming

The wrinkling behavior of a thin sheet with perfect geometry is associated with compressive instability. The compressive instability is influenced by many factors such as stress state, mechanical properties of the sheet material, geometry of the body, contact conditions and plastic anisotropy. The analysis of compressive instability in a plastically deforming body is difficult considering all the factors because the effects of the factors are very complex and the instability behavior may show a wide variation for a small deviation of the factors. In this study, the bifurcation theory is introduced for the finite element analysis of puckering initiation and growth of a thin sheet with perfect geometry. All the above mentioned factors are conveniently considered by the finite-element method. The instability limit is found by the incremental analysis and the post-bifurcation behavior is analyzed by introducing the branching scheme proposed by Riks. The finite-element formulation is based on the incremental deformation theory and elastic–plastic material modeling. The finite-element analysis is carried out using the continuum-based resultant shell elements considering the anisotropy of the sheet metal. In order to investigate the effect of plastic anisotropy on the compressive instability, a square plate that is subjected to compression in one direction and tension in the other direction is analyzed by the above-mentioned finite-element analysis. The critical stress ratios above which buckling does not take place are found for various plastic anisotropic modeling methods and discussed. Finally, the effect of plastic anisotropy on the puckering behavior in the spherical cup deep drawing process is investigated. From the results of the finite-element analysis, it is shown that puckering behavior of sheet metal is largely affected by plastic anisotropy.     

Modelling of the internal stress in dislocation cell structures

The nonuniform distribution of dislocations in metals gives rise to material anisotropy and internal stresses that determine the mechanical response. This paper proposes a micromechanical model of a dislocation cell structure that accounts for the material inhomogeneity and incorporates the internal stresses in a physically-based manner. A composite model is employed to describe the material with its dislocation cell structure. The internal stress is obtained as a natural result of plastic deformation incompatibility and incorporated in the composite model. Applications of this model enable the prediction of the mechanical behavior of metals under various nonuniform deformations. The implementation of the model is relatively straightforward, allowing easy use in macroscopic engineering computations.     

纤维增强韧性基体界面力学行为

分析了纤维增强韧性基体的界面力学行为及其失效机理,按剪滞理论和应变理化规律研究微复合材料的弹塑性变形和应力状态,讨论了幂硬化和线性硬化基体的弹塑性变形和界面应力分布,并给出纤维应力和位移的表达式。按最大剪应力强度理论建立了纤维／基体界面失效准则,推导出弹塑性界面失效的平均剪应力随纤维埋入长度的变化关系。     

A Mixed Criterion of Delayed Creep Failure Under Plane Stress

The paper discusses delayed creep failure criteria and their experimental justification. These criteria allow transition from the strength characteristics under uniaxial stress to the strength characteristics under plane stress. The criterion is chosen in the form of a mixed invariant that relates two stress components responsible for brittle and ductile failure. The limit characteristics take the effect of the principal stresses into account. The criterion was tested for isotropic metallic materials subjected to internal pressure, internal pressure with tension, pure torsion, and tension with torsion     

岩土的一种强度准则及其变换应力法

基于岩土摩擦性,假设岩土破坏是由其物理空间内特征面上的应力比决定,提出了等效应力比的概念,即物理空间特征面上的剪应力合力与正应力合力的比值.在二维条件下,等效应力比可表示为σ-τ坐标系下与摩尔圆相切的直线扣除截距正切值;在三维条件下,假设在XYZ空间内存在一三维物理空间平面,此三维空间特征平面的等效应力比为影响材料强度特性的决定性因素,基于上述三维空间特征面建立了强度准则并称之为a准则.SMP准则以及广义Mises准则都是a准则的特例,当二维坐标中的截距为零时,则强度准则退化为SMP(spatially mobilized plane)强度准则,而当正切角为零时,则强度准则退化为广义Mises准则.而当截距与外切角均不为零时,则强度准则为介于上述两者之间的一种强度准则,在偏平面上为介于SMP曲边三角形与广义Mises圆形之间的曲边三角形.在子午面上,采用考虑岩土压剪耦合的屈服准则,破坏准则采用幂函数表达式.在偏平面上提出了基于a准则的形状函数,并采用真三维应力状态表示的破坏强度准则表示在三轴压缩路径下以p,q二维应力变量表达的准则公式,推导得到了基于a准则的变换应力公式,可简单地将一般以p,q为基本变量的二维模型转变为三维应力模型.通过强度以及多种应力路径的测试对比,验证了a准则及基于该准则的变换应力公式的合理性.