Tri-axial deformation of a plastic-rigid solid

The paper deals with the deformation of an ideal plastic solid that is initially rigid, i.e., elastic deformations are neglected. In addition, the solid flows by means of the mechanism of extended slip, for which the rotation-rate vector field remains continuous and the strain-rate tensor is solenoidal. The Tresca yield criterion applies to such a solid and with an associated flow-rule is represented in a manner that includes both bi-axial and tri-axial states of strain. Two new theorems are proved, and a second-order partial differential equation is derived for the first invariant of the stress tensor (hydrostatic pressure); the analogue of a similar published equation for the bi-axial strain case. To illustrate the methodology, the above theory is applied to the tri-axial problem of a thick metal plate clamped round a circle and deflected by means of pressure. It is shown, from the exact solution, that the errors due to the use of the approximate membrane formula for a clamped thin plate are small, even for a 6mm thick plate clamped on a circle 100mm in diameter. Surprisingly, there is an initial thickening of the plate and it is shown that, regardless of the plate thickness, the pressure passes through a maximum at a deflection equal to \({1/\sqrt{3}}\) of the radius of the clamping circle.     

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

A local constitutive model for anisotropic granular materials is introduced and applied to isobaric (homogeneous) axial-symmetric deformation. The simplified model (in the coordinate system of the bi-axial box) involves only scalar values for hydrostatic and shear stresses, for the volumetric and shear strains as well as for the new ingredient, the anisotropy modulus. The non-linear constitutive evolution equations that relate stress and anisotropy to strain are inspired by observations from discrete element method (DEM) simulations. For the sake of simplicity, parameters like the bulk and shear modulus are set to constants, while the shear stress ratio and the anisotropy evolve with different rates to their critical state limit values when shear deformations become large. When applied to isobaric deformation in the bi-axial geometry, the model shows ratcheting under cyclic loading. Fast and slow evolution of the anisotropy modulus with strain. Lead to dilatancy and contractancy, respectively. Furthermore, anisotropy acts such that it works “against” the strain/stress, e.g., a compressive strain builds up anisotropy that creates additional stress acting against further compression.     

Characterization of Bi-axial fatigue resistance of polymer plates

An approach is proposed to characterize bi-axial fatigue resistance of polymer plates. The method proposed here can detect a change of mechanical properties of polymers (especially ductility) due to fatigue loading, before any visible crack is generated. A decrease in ductility by fatigue loading has been reported for polymers subjected to uni-axial fatigue stresses. Whether a similar phenomenon occurs under bi-axial fatigue stresses is not known at present. In this study, a new bi-axial testing device was designed and built that is capable of applying equal bi-axial forces to cruciform specimens in a cyclic mode. This paper details the test method, including design and instrumentation of the bi-axial testing device, specimen design, and the procedure to determine the load for a desired bi-axial stress state. Poly(acrylonitrile-butadiene-styrene) (ABS) was used as the sample material. Preliminary results reported here show that the ABS’s ductility can be reduced significantly by applying 500 cycles of bi-axial fatigue stress at a level that is about 50% of its tensile strength. The results also indicate that such a level of bi-axial fatigue stress has induced extensive rubber particle cavitation, though it is yet to clarify whether the particle cavitation has led to the ductility drop. The study concludes that the methodology proposed in this paper can be used to evaluate bi-axial fatigue resistance of polymer plates for the purpose of materials evaluation.     

建筑膜材料双轴向拉伸弹性常数的估算方法

以机织物增强建筑膜材料为对象,研究了通过单轴向拉伸试验来获取双轴向拉伸弹性常数的方法。根据膜材料双轴向拉伸弹性模量的确定方法,以二维正交各向异性材料的本构关系为基础,以膜材料经纬向拉伸应力比为设定加载参数,导出了机织膜材料单轴向和双轴向拉伸弹性模量之间的关系,提出了采用单轴向拉伸弹性常数估算建筑膜材料双轴向拉伸弹性常数的方法。通过参考文献中对GF/PTFE和PVDF1202T膜材料拉伸试验的测试结果,验证研究所提出方法的适用性。结果表明,在工程实践中利用单轴向拉伸试验来获得膜材料双轴向拉伸弹性模量是可行的。     

再生混凝土三轴受压力学性能试验研究

为了研究再生混凝土在三轴应力状态下的力学性能,以再生骨料取代率和围压值为变化参数,设计了36个圆柱体试件,采用位移控制的加载方式进行常规三轴试验。通过试验观察了试件的破坏形态,获取试件受力破坏全过程应力-应变曲线以及峰值应力、峰值应变等特征参数,分析了再生骨料取代率和围压值对再生混凝土三轴受压力学性能的影响,提出了侧向围压值与初始弹性模量、竖向峰值应力、峰值应变之间的关系公式。研究结果表明：取代率对三轴受力再生混凝土的峰值应力和峰值应变影响不大,与天然混凝土相比,其变化分别在5%和2%的范围内波动,而取代率对再生混凝土的初始弹性模量有较大的影响,与天然混凝土相比,三轴受力再生混凝土的弹性模量提高了20%左右;侧向围压值对三轴受力再生混凝土的各项性能指标影响显著,增大围压值能有效提高再生混凝土的弹性模量、承载能力和变形性能。研究结果为再生混凝土的进一步科学研究和推广应用提供参考。     

A survey of test methods for multiaxial and out-of-plane strength of composite laminates

This review paper gives an overview of test methods for multiaxial and out-of-plane strength of composite laminates, with special consideration of non-crimp fabrics (NCF) and other textile systems. Tubular and cruciform specimens can provide arbitrary in-plane loading, while off-axis and angle-ply specimens provide specific biaxial loadings. Tensile and compressive out-of-plane strength may be determined by axial loading of specimens with a waisted gauge section, while bending of curved specimens allow determination of the out-of-plane tensile strength. Tests suited for out-of-plane shear strength include the short beam shear test, the inclined double notch test and the inclined waisted specimen. Testing of arbitrary tri-axial stress states using tubular or cruciform specimens with superimposed through-the-thickness loading is highly complex and significant problems have been reported in achieving the intended stress states and failure modes. Specific tri-axial stress states can be obtained by uniaxial loading of specimens with constrained expansion, as in the die channel test.     

冻融循环后粉煤灰陶粒混凝土定侧压下的强度和变形性能试验研究

利用混凝土静、动三轴试验系统,完成了粉煤灰陶粒混凝土立方体试件在4组不同冻融循环次数、4种恒定侧压下的双轴压压强度和变形性能试验。考察了不同侧压应力水平下试件的破坏形态和试件表面裂缝分布及走向特征。测量了4种侧压应力水平下的极限抗压强度及两个加载方向的应变值,并根据试验结果系统分析了定侧压下粉煤灰陶粒混凝土双轴压压极限强度和变形性能(包括峰值应变、应力-应变关系曲线、弹性模量)随冻融循环次数和侧压应力水平的变化规律,建立了考虑冻融循环次数和侧压应力水平的主应力空间的双轴压压强度准则,为寒冷海洋环境条件下粉煤灰陶粒混凝土结构在经受双轴压压荷载作用时的强度分析提供试验和理论依据。     

Deep drawing behaviour of ultrafine grained copper: modelling and experiment

Ultrafine grained materials produced by severe plastic deformation methods possess attractive mechanical properties such as high strength compared with traditional coarse grained counterparts and reasonable ductility. Between existing severe plastic deformation methods the Equal Channel Angular Pressing is the most promising for future industrial applications and can produce a variety of ultrafine grained microstructures in materials depending on route, temperature and number of passes during processing. Driven by a rising trend of miniaturisation of parts these materials are promising candidates for microforming processes. Considering that bi-axial deformation of sheet (foil) is the major operation in microforming, the investigation of the influence of the number of ECAP passes on the bi-axial ductility in micro deep drawing test has been examined by experiments and FE simulation in this study. The experiments have showed that high force was required for drawing of the samples processed by ECAP compare to coarse grained materials. The limit drawing ratio of ultrafine grained samples was in the range of 1.9–2.0 with ECAP pass number changing from 1 to 16, while a higher value of 2.2 was obtained for coarse grained copper. However, the notable decrease in tensile ductility with increase in strength was not as pronounced for bi-axial ductility. The FE simulation using standard isotropic hardening model and von Mises yielding criterion confirmed these findings.     

A constitutive model for the deformation induced anisotropic plastic flow of metals

A mathematical framework is established for the equations governing inelastic deformation under multi-dimensional stress states and for the associated evolution equations of the internal state variables. The formulation is based on a generalization of the Prandtl-Reuss flow law. In the evolution equations for the inelastic state variables that control plastic flow, it is assumed that part of the rate of change is isotropic and the remaining part varies according to the sign and orientation of the current rate of deformation vector. This leads to a minimum of twelve components of the internal state tensor which represents resistance to inelastic deformation. In this manner, both initial and load history induced plastic anisotropy can be modeled. A specific set of equations for anisotropic plastic flow is developed consistent with the inelastic state variables.     

Some comments on surface cracks in rails

The present work considers the problem of whether a shallow angle surface crack on a rail may propagate either parallel or perpendicular to the surface. After referring to a classification of crack‐like defects, a distinct surface crack with a typical length of 1 mm and more, inclined to the surface by an angle of approx. 30°, is introduced. Then various strain and stress states are discussed (eigenstress, residual and load stress state) which may control the crack growth. Stress intensity factor equations are provided for the internal and load stress states. In particular, the deformation process due to a single pass (overrolling) by a wheel is investigated. Recommendations are presented on how to relate the stress intensity factor ranges to the actual deformation process. For a typical loading condition, the positive part of the mode I stress intensity factor range is near to the effective threshold value of a rail steel. The influence of the material and its strength on the crack propagation behaviour is discussed qualitatively.     

基于统一强度理论的厚壁套管柱三轴抗拉强度

为了研究油气井厚壁套管柱的力学性能,基于统一强度理论,合理考虑中间主应力和材料拉压比的影响,推导了厚壁套管柱三轴抗拉强度的计算公式,分析了内外压比、材料的拉压比、中间主应力和径厚比等因素对不同工况下套管柱三轴抗拉强度的影响特性。研究结果表明：强度准则的选用对套管柱的三轴抗拉强度具有显著影响;材料拉压强度不等特性(SD效应)对套管柱的三轴抗拉强度也具有显著影响,当内外压比小于或等于1时,套管柱的三轴抗拉强度随材料拉压比的增大近似线性提高,当内外压比大于1时,材料SD效应的影响与外荷载有关;考虑中间主应力效应可以充分发挥材料的自承载能力和强度潜能,提高套管柱的三轴抗拉强度,具有一定的经济效益;内外压比和径厚比对套管柱的三轴抗拉强度也具有一定的影响。该文计算公式适用于具有SD效应和中间主应力效应的材料,并将多种屈服准则下套管柱三轴抗拉强度的表达式统一起来,具有广泛的适用性,可为油气井厚壁套管柱的设计提供借鉴。     

MEASUREMENT OF NON-UNIFORM BI-AXIAL RESIDUAL STRESSES BY THE HOLE DRILLING METHOD

The hole drilling method is used to evaluate bi-axial residual stresses varying with depth. Equations with experimentally determined calibration constants, given here for light-alloys, relate residual stresses to strain relaxations as the hole is drilled. Accuracy and limitations are assessed by application to known stress conditions. The method can be used on large structures and in field conditions.     

Stochastic progressive failure analysis of laminated composite plates using Puck's failure criteria

The present work deals with second-order statistics of the progressive failure response of laminated composite plates subjected to in-plane uniaxial and bi-axial loadings with random system properties. A stochastic finite element method based on higher-order shear deformation theory combined with first- and second-order perturbation technique is used for solution of random progressive failure equation. A Puck failure criterion is used for the evaluation of first ply and last-ply failure load. The results obtained using the present solution approach are validated with the results available in the literature and Monte Carlo simulation.     

Effect of aspect ratio on large deformation and necking of polyethylene

Objective of the study is to examine influence of aspect ratio of rectangular cross-section on the tri-axial stress state developed by necking in tensile specimens of polyethylene. The first part of the paper presents an experimental study that used two types of high-density polyethylene (HDPE) as sample material to identify the thickness-dependent relationship between engineering stress and elongation from tensile tests. The experimental study also shows that thinner specimens, i.e. higher aspect ratio, have lower neck propagation speed and higher flow stress, thus higher rate of energy consumption for the neck propagation. The second part of the paper presents finite element simulation of large deformation and necking in HDPE when subjected to uni-axial tension. True stress–strain relationship and governing equation for visco-plastic deformation are determined from the finite element simulation based on experimental data for the two HDPEs, which reveals influence of aspect ratio of cross-section on the stress state during the necking process. Results from the study indicate that plane-stress condition prevails when the aspect ratio increases, i.e. by decreasing the specimen thickness. The finite element simulation also supports the observation that necking in specimens with higher aspect ratio, i.e. thinner specimens, generates higher percentage of reduction in the thickness direction but lower in the width direction. The overall capability for the deformation endurance was found to improve by reducing the specimen thickness. The paper concludes that finite element simulation has successfully demonstrated the influence of aspect ratio of the cross-section on the stress state in the necking process. The paper also concludes that by combining experimental testing and finite element simulation, time-dependent deformation behaviour can be separated from the time-independent deformation behaviour, which is almost impossible to achieve based on the experimental techniques that rely purely on measurement only.     

横肋波纹钢板-方钢管混凝土组合柱双向偏压力学性能研究及承载力计算

为研究横肋波纹钢板-方钢管混凝土组合柱的双向偏压力学性能,对两根横肋波纹钢板-方钢管混凝土组合柱试件展开了双向偏压加载试验,探究了不同偏心距对试件在双向偏压荷载下的荷载-变形曲线、破坏模态和截面应变发展状况的影响,分析了波纹板与钢管、混凝土之间的相互作用机理.在试验基础上运用有限元模拟,分析了偏心距、加载角度、钢管厚度...     

Remarks on elastic buckling for sectorial plates

This work investigates the edge-buckling experienced by a sectorial plate in a uniform bi-axial state of stress and subject to in-plane bending. Since the governing differential equations have variable coefficients, it turns out that the neutrally stable eigenfunctions can be qualitatively quite different as the mode number varies. Our interactive boundary-layer analysis succeeds in capturing the most dangerous mode associated with the global minimum of the marginal stability curve, while a complementary WKB route supplies an explanation for the morphological transitions experienced by the eigenmodes. The validity of our analysis is confirmed by direct numerical simulations of the full fourth-order buckling equation, which are in excellent agreement with the theoretical considerations.     

Generalised constitutive equations for densification of metal matrix coated fibre composites

Abstract

The present paper completes a study of constitutive equations for the consolidation processing of continuous fibre reinforced metal matrix composite materials. It builds on an earlier paper in which physically based constitutive equations were derived for the case of symmetrical, isostatic loading. In the present paper, constitutive equations are developed for in plane, general stress states. The total deformation of the consolidating composite is expressed as the sum of a conventional deviatoric creep term, together with a dilatational term, which was derived using a variational method previously published. The equations contain only two material parameters, which are the conventional creep coefficient and exponent for the fibre coating material (in this case, Ti-6Al-4V). The resulting equations have been implemented into finite element software enabling the simulation of practical consolidation processes. The model has been verified by comparing predicted results with those obtained from independent micromechanical models. A number of experimental tests have been carried out, and the model is used to predict the rates of densification for a range of experimental pressure and temperature histories. Good comparisons have been achieved.     

Micromechanical constitutive modelling of granular media: Evolution and loss of contact in particle clusters

Micromechanical constitutive equations are developed which allow for the broad range of interparticle interactions observed in a real deforming granular assembly: microslip contact, gross slip contact, loss of contact and an evolution in these modes of contact as the deformation proceeds. This was accomplished through a synergetic use of contact laws, which account for interparticle resistance to both sliding and rolling, together withstrain-dependent anisotropies in contacts and the normal contact force. By applying the constitutive model to the bi-axial test it is demonstrated that the model can correctly predict the evolution of various anisotropies as well as the formation of a distinct shear band. Moreover, the predicted shear-band properties (e.g. thickness, prolonged localisation, void ratio) are an even better fit with experimental observations than were previously found by use of previously developed micromechanical models.     

Micromechanical constitutive modelling of granular media: evolution and loss of contact in particle clusters

Micromechanical constitutive equations are developed which allow for the broad range of interparticle interactions observed in a real deforming granular assembly: microslip contact, gross slip contact, loss of contact and an evolution in these modes of contact as the deformation proceeds. This was accomplished through a synergetic use of contact laws, which account for interparticle resistance to both sliding and rolling, together with strain-dependent anisotropies in contacts and the normal contact force. By applying the constitutive model to the bi-axial test it is demonstrated that the model can correctly predict the evolution of various anisotropies as well as the formation of a distinct shear band. Moreover, the predicted shear-band properties (e.g. thickness, prolonged localisation, void ratio) are an even better fit with experimental observations than were previously found by use of previously developed micromechanical models.