An anisotropic creep damage model for multiaxial cyclic loading histories

The purpose of this study is the development of an anisotropic creep damage theory within the continuum damage mechanics, applicable to creep-dominated cyclic loading histories. A damage distribution is expressd in rate form as a symmetric tensor of rank necessary to match physically measured damage. A theoretical model which expresses general anisotropic creep damage phenomena with power law cavity growth is proposed. The coupling of damage with a bounding surface cyclic viscoplasticity theory is also accomplished. Comparison with experimental results are made for weakly anisotropically damaging materials, type 304 stainless steel at 593°C. Good correlation of rupture time, secondary creep, and tertiary creep has been obtained for proportional and nonproportional, isothermal, constant isochronous nominal stress loading histories. A modification of the isochronous stress (the set of stress state which have a same rupture time) for compressive hydrostatic stress state has been offered.     

Modeling of anisotropic plastic behavior of ferritic stainless steel sheet

Modeling of anisotropic plastic behavior of ferritic stainless steel sheet (Type 409) was investigated using the three yield functions of Hill [A theory of the yielding and plastic flow of anisotropic metals. Proceedings of Royal Society of London, Series A 1948;193:281–97.], Barlat and Lian [Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions. International Journal of Plasticity 1989;5:51–66] and Barlat et al. [Plane stress yield function for aluminum alloy sheet. Part I: Theory. International Journal of Plasticity 2003;19:1297–319.] (referred to as Yld2000-2d) criteria. Mechanical behaviors were characterized based on uniaxial tension, balanced biaxial bulge, and disk compression tests. Directionalities of yield stresses and r values were predicted from the three criteria and compared with experimental results. In order to verify the modeling accuracy of the three functions under complex loading conditions, cylindrical cup drawing and limiting dome height tests were carried out numerically and experimentally. It has been demonstrated that the result from Yld2000-2d criterion exhibits good agreement with experimental data. The effects of anisotropic hardening on earing and necking were also investigated based on the different levels of plastic work.     

Constitutive modelling of the anisotropic creep behaviour of nickel-base single crystal superalloys

This paper focuses on the modelling of primary, secondary and tertiary creep of nickel-base single crystal superalloys at high temperatures. In particular, we propose an extension of the Cailletaud single crystal plasticity model [Méric L, Poubanne P, Cailletaud G. Single crystal modeling for structural calculations: part I—model presentation. Transactions of the ASME 1991;133:162-170] to include tertiary creep. This is achieved by introducing an additional evolution equation for a scalar damage variable per slip system. In addition, a methodology for the calibration of the material parameters of the model to fit the results from experiments has been implemented. The parameter identification rests upon a two-membered evolution strategy. The comparison with uniaxial and multiaxial test data shows a good agreement between model and experiment. The structural simulations have been performed by means of a special element technology which enables efficient and accurate finite element computations.     

A methodology for smoothing of point cloud data based on anisotropic heat conduction theory

It is necessary to smooth point cloud data in reverse engineering or the inspection of free-form surfaces because noisy points will have a negative influence on the post-processing of this data. The big problem in smoothing point cloud data is how to solve the dilemma between removing noisy points and keeping feature boundary information, whilst controlling the diffusiveness of noisy points. In this paper, the theory of anisotropic heat conduction is adopted to establish a mathematical model of point cloud data smoothing. The point cloud data can be considered as a temperature field with an adiabatic boundary. So the heat is only conducted inside the temperature filed and has no effect on the outer side. For point cloud data, it means that the smoothing is only on the local area, which makes a good balance between deleting noisy points and keeping feature boundary information. The method has been implemented by using two cases for practical application, and the result proves its efficiency.     

Shakedown theory for elastic-perfectly plastic bodies revisited

Yield criteria for elastic-perfectly plastic solids, in particular, the Mises and Tresca ones, permit unlimited hydrostatic stresses, leading to some singularity in the classical Melan–Koiter shakedown theory. Classical shakedown theory is re-examined regarding this problem. It is shown that the complete proofs of both static and kinematic theorems require restrictions on the hydrostatic stresses. A modified shakedown kinematic theorem using a fictitious material that can yield in bulk tension and compression has been constructed for subsequent treatment of real engineering materials, which cannot yield but fail under high hydrostatic stresses. The kinematic theorem should have vanishing hydrostatic plastic strain rate solution for the safety of the body against hydrostatic fracture. In this way, the modified kinematic formulation including the limits on hydrostatic stresses are suggested for application. The modifications are also naturally added into the plastic limit theory, which is a limiting case of the shakedown one. Also in the paper, the kinematic approach is used to deduce some simplified estimates for specific non-shakedown collapse modes of elastic plastic structures.     

Development of an anisotropic constitutive model for single-crystal superalloy for combined fatigue and creep loading

A unified anisotropic viscoplastic constitutive model for single-crystal superalloys is developed based on a modification of a phenomenological isotropic model. Orientation-dependent viscoplastic behaviour was observed in experiments. The model is used to simulate the orientation and cyclic mechanical response of single-crystal SRR99 under combined fatigue and creep conditions at 950°C. The results from the simulations are then used to estimate the fatigue-creep lives of the single-crystal nickel-base superalloy SRR99 using a new life prediction methodology. The predicted fatigue-creep lives are in good agreement with the experimental results.     

A study of the plastic buckling of axially compressed cylindrical shells with a thick-shell theory

A thick shell theory is used to calculate the critical load of plastic buckling of axially compressed cylindrical shells. The buckling equations are derived with the principle of virtual work on the basis of a transverse shear deformable displacement field. The deformation theory of plasticity is used for constitutive equations. To fit the uniaxial stress–strain curve, the Ramberg–Osgood equation is used. In the numerical examples special attention is paid to the dependence of the buckling mode on the ratios of radius to thickness R/h and length to radius L/R. This dependence divides the (R/h,L/R)-plane into simply connected regions each of which corresponds to a buckling mode. These regions form a “buckling mode map”.     

塑料模具的磨损机制与失效机理的研究

通过对塑料模使用过程中表面磨损机制和失效机理的研究,得出造成塑料模具尺寸精度和表面粗糙度下降的原因,提出提高塑料模具抗磨损的措施.实践证明,这些措施能很好消除塑料模具磨损现象,从而提高了塑料模具寿命和生产产品的质量.     

An anisotropic damage-based plastic yield criterion and its application to analysis of metal forming process

Based on the continuum damage mechanics (CDM), both the total damage growth force and the damage equivalent stress has been firstly derived. Material and damage are considered to be anisotropic in this theoretical model. A new damage-based plastic yield criterion, where the damage equivalent stress is taken as the yield function, and the corresponding damage evolution equation has been established. A relation between the damage variable and the plastic deformation has been proposed. This relation can be applied to obtain the damage history in terms of Moiré photo-mechanics technology in this work. In addition, from the anisotropic damage-based plastic yield criterion presented, the large-scale finite element codes ABAQUS/Explicit in conjunction with the damage experimental results has been then used to calculate some mechanical variable fields in metal forming process. It has finally been verified that the position corresponding to the maximum value in damage equivalent stress field accurately coincides with the initial place of macro-crack given by Erichsen cupping tests carried out by authors.     

TRIZ理论下塑料射出成型机构的创新设计

射出成型法是最常见的塑料加工法,广泛应用于航空、通讯、光电、医疗和半导体等产业中.但是在应用过程中出现了很多设计问题,TRIZ理论为设计者提供了很好的创新解决方法.通过建立相应的知识库和应用相关的矛盾解决方法,对设计中存在的问题进行解决.通过对塑料射出成型机构的CATIA模型进行产品功能定义和产品功能的最优化的处理,对存在的问题进行了创新设计.     

An exact solution for the elastic/plastic bending of anisotropic sheet metal under conditions of plane strain

A theoretical analysis for the elastic/plastic bending of sheet metal exhibiting a state of normal anisotropy is considered in this paper, assuming a plane strain condition to exist in the deformation process. The material is supposed to yield according to Hill's quadratic yield criterion and its associated normality rule of plastic flow. The relationship between the bending couple and the curvature of the bent sheet is presented in a graphical form that reveals the influence of anisotropy and strain-hardening on the bending characteristic of the sheet metal. The results indicate that the elementary bending theory significantly overestimates the magnitude of the bending couple to produce a given elastic/plastic curvature of the bent sheet.     

A new mechanism of plastic flow

When ductile materials are tested in simple shear, with moderate amounts of compressive stress on the shear plane, what appears to be negative strain hardening occurs at relatively large strains. These results are in apparent contradiction to the commonly held views that metals strain harden without saturation to the highest values of strain and that compressive stress on the shear plane does not influence flow stress.A new mechanism of plastic flow is presented that involves the formation and rewelding or microcracks of limited extent on shear surfaces. Possible applications of the new theory to metal cutting and geological events are briefly discussed.     

A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)—I

It is shown from various view points that many of the disadvantages of the conventional theory based on a quadratic yield function can be satisfactorily removed by the use of a yield function of fourth order. Incremental equivalent strain $\text{d}\text{?}{}_{\mathrm{eq}}$is defined by $\text{d}\text{?}{}_{\mathrm{eq}}\text{=σ}{}_{\mathrm{ij}}\text{d}\text{?}{}_{\mathrm{ij}}\text{σ}{}_{\mathrm{eq}}$, and cannot generally be expressed simply by the strain increment components d?_ij. In contrast with the conventional theory, coefficients in the yield function f cannot be determined from the r-values only in uniaxial tensile tests, but yield stresses in these tests and for example in an equi-biaxial tension for the same $\text{}\text{?}\text{ge}{}_{\mathrm{eq}}$ are also required. This fact ensures that the $\text{σ}{}_{\mathrm{eq}}\text{?}\text{?}{}_{\mathrm{eq}}$ curve for arbitrary loading is uniquely determined by the uniaxial tension curve in the rolling direction (R.D.), and thus such an intrinsic difficulty of the conventional theory as dependence of the $\text{σ}{}_{\mathrm{eq}}\text{?}\text{?}{}_{\mathrm{eq}}$ curve on types of loading does not arise. Some formulae for the determination of the coefficients in f are given. Relationships between types of earing in axi-symmetrical deep-drawing and the coefficients of f are examined in detail and it is emphasized that only very special cases are included in the conventional yield function and thus use of it is very limited.     

A continuum mechanics for damaged anisotropic solids

This paper develops a theory of continuum damage mechanics for anisotropic solids on the basis of both the strain energy equivalence principle and the equivalent (fictitious) line crack damage modeling. The strain energy equivalence principle is used to develop the effective continuum elastic properties of a damaged solid in terms of the undamaged anisotropic elastic properties and a scalar damage variable. The equivalent line crack representation of local damage provides, a means by which the effective direction of damage propagation can be identified from the local stresses and strains that are available in the course of continuum damage analysis. A scalar damage variable is defined as the effective volume fraction of a damaged zone associated with an equivalent line crack. Finally, an iterative numerical approach to continuum damage analysis is introduced.     

各向异性湿法刻蚀z切石英后结构侧壁形貌的预测

基于石英晶体各晶面的湿法刻蚀速率,研究了石英微结构侧壁形貌的预测方法,讨论了各向异性湿法刻蚀石英的规律.首先,总结了石英各主要晶面的相对刻蚀速率,分别绘制了x、y族刻蚀速率矢量图.然后,在掩模层的边缘处,通过绘制相应的晶面刻蚀速率矢量图,得到各速率矢量的晶面线,晶面线所围成的最小轮廓即是石英微结构的刻蚀形貌.最后,利用该方法预测了x向和y向石英梁的侧壁形貌.在70℃的氢氟酸和氟化铵混合溶液内刻蚀5h,制作了厚度均为500μm的x向和y向两种石英微梁.结果显示,y向梁的-x向侧壁有一均匀整齐的晶棱,棱高210 μm,而+z向侧壁平滑.x向梁的侧壁均有晶棱,+y向晶棱较大,棱高为450 μm,-y向晶棱棱高为240 μm.所制作梁的侧壁形貌与预测结论基本吻合,验证了预测方法的正确性.基于该方法可在石英微结构的设计阶段,通过引入工艺因素对微结构进行优化.     

A theory of plastic anisotropy based on yield function of fourth order (plane stress state)—II

It is shown from various view points that many of the disadvantages of the conventional theory based on a quadratic yield function can be satisfactorily removed by the use of a yield function of fourth order. Incremental equivalent strain is defined by , and cannot generally be expressed simply by the strain increment components d_ij. In contrast with the conventional theory, coefficients in the yield function f cannot be determined from the r-values only in uniaxial tensile tests, but yield stresses in these tests and for example in an equi-biaxial tension for the same are also required. This fact ensures that the curve for arbitrary loading is uniquely determined by the uniaxial tension curve in the rolling direction (R.D.), and thus such an intrinsic difficulty of the conventional theory as dependence of the curve on types of loading does not arise. Some formulae for the determination of the coefficients in f are given. Relationships between types of earing in axi-symmetrical deep-drawing and the coefficients of f are examined in detail and it is emphasized that only very special cases are included in the conventional yield function and thus use of it is very limited.     

Fatigue properties of fine grained magnesium alloys after severe plastic deformation

Fine grained AZ31 and AZ61 magnesium alloys produced by equal channel angular pressing (ECAP) were tested for investigating tensile and fatigue properties, including microstructure, monotonic tensile flow, fatigue life and crack growth rate. For the two alloys, the yield stress of the ECAPed sample was lower than that of the unECAPed (=as received) sample, because of the fact that the softening effect due to texture anisotropy overwhelmed the strengthening effect due to grain refinement. Grain refinement of the AZ31 and AZ61 alloys through ECAP was found not to be significantly effective in increasing fatigue strength.     

A practical approach to the stereology of anisotropic structures

Inversion formulae for the rose of directions of fibre (surface) processes are evaluated by means of a parametric model of the rose of intersections. The problems of statistical tests of isotropy, degree of anisotropy and stereological formulae are solved. A short-cut sampling procedure for the three-dimensional case is proposed and applied in a metallographic situation.     

A graphical technique for constructing anisotropic slip-line fields

A completely graphical procedure for constructing plane strain slip-line fields for anisotropic materials, with arbitrary convex yield loci, is described. It can be viewed as a generalization of Prager's well-known procedure for isotropic materials. In illustration the method is applied to the problem of compression of a finite strip between perfectly rough parallel dies. In addition the corresponding analytical solution for an infinite strip is found for an arbitrary yield condition.