Two systems for automatic reduction of time-dependent photomechanics data

Time-dependent photomechanical model materials will not, in general, exhibit a one-to-one relationship between the instantaneous stress and the relative retardation. Due to the complicated nature of this relationship, it is often more accurate to use the analog method of data reduction. This method consists of reproducing the fringe-order history observed in the model in a tensile specimen of the model material and recording the corresponding stress history. Two servo systems are described in this report which may be programmed to produce a desired fringe-order history in a time-dependent tensile specimen.     

Mechanical and optical characterization of cellulose acetate

To obtain the basic relations for photo-viscoelastoplastic stress analysis using cellulose acetate, the effect of strain rate as well as room temperature on mechanical and optical properties was precisely investigated by the uniaxial tension test. As a result, the nonlinear stress-strain, the non-linear-stress-fringe order and the nonlinear-fringe-order strain relations were uniquely reoresented in their nondimensional forms regardless of strain rate and room temperature. Young's modulus, yield stress and the yield fringe order were linearly related both to room temperature and to logarithm of strain rate. The effect of strain rate on these relations has caused great difficulties in experimental stress analysis with respect to photoplasticity. However, it was found in this work that the value of the strain rate at any points in the model can be determined by the fringe-order rate measured. Therefore, it is possible to estimate not only the distribution of strain rate but that of stress or strain in the photo-viscoelastoplastic model with cellulose acetate.     

A multilayer-reflection technique for three-dimensional photoelastic studies of perforated plates in bending

A photoelastic investigation was conducted to determine the stress-concentration factors around a large, symmetrically reinforced central hole in a square plate under 1∶1 and 2∶1 biaxial bending. Tapered-edge rings served as the reinforcement, and a major objective was to determine the ring proportions such that the maximum stress at the hole would be equal to the value which would be present in an unperforated plate under the same nominal stress. Because the stress distribution at the periphery of a hole in such a plate structure varies in the radial, tangential and thickness direction, it was necessary to employ a three-dimensional photoelastic technique. There were a number of serious disadvantages in the use of any of the standard procedures and a new three-dimensional technique for room-temperature use was developed which is particularly suitable for the determination of boundary stresses around holes in bending experiments. With the technique in its present state of development, the three-dimensional isochromatic distribution in the plate can be determined from a single model and, from this, the boundary value of stress. The new technique utilized a laminated-plate model. Selective aluminizing of the laminations allowed for the determination of fringe-order distributions in the thickness direction as well as in the radial and circumferential directions at the boundary of the hole in flat models. Uniaxial maximum fringe orders were determined and, from these, the biaxial values were obtained by superposition.     

Determining isoclinics from fringe patterns

A procedure has been developed which imparts new flexibility and increased usefulness to the bonded-polariscope technique. It also may help to increase the precision of the shear-difference method of principal-stress separation by providing greater precision to the determination of principal-stress directions. The procedure involves bonding a uniaxially stress-frozen plate of model material into a model between Polaroid sheets to function as a bonded polariscope. The fringe data obtained under load provide information for determining the principal-stress directions throughout the model by solution of a simple algebraic relation which lends itself readily to accurate plotting for graphical analysis. The inherent precision should exceed that of isoclinic analysis, particularly in regions where indistinct isoclinics might be expected, since accuracy increases with loading. Accurate fringe-order data also can be obtained by plotting fringe order as a function of position. The basis for the procedure is the modification of the applied-stress field by the presence of the residual (frozen)-stress field. Furthermore, the frozen-fringe order combines with the fringes applied at room temperature as though both stress fields were applied at room temperature. Theory and experimental confirmation are presented, together with a sample principal-stress map which is compared with that obtained from theory, and also from isoclinics. In addition, the chart for rapid graphical solution is included.     

混凝土拉伸断裂的细观数值分析

根据混凝土试件拉伸和三点弯曲的物理模型,用梁-颗粒模型BPM 2D(B eam-Particle M ode l)模拟了混凝土拉伸和三点弯曲试件微裂纹的萌生、扩展直至试件宏观破坏的全过程。在梁-颗粒模型中用三种类型梁单元形成混凝土细观数值模型,每种类型梁单元的力学性质均按韦伯(W e ibu ll)分布随机赋值以模拟混凝土细观结构的非均匀性。数值模拟结果给出了混凝土拉伸应力-应变曲线和三点弯曲载荷-位移曲线,以及混凝土试件破坏过程最大应力分布图和裂纹扩展图。数值模拟结果显示混凝土破坏过程实际上就是微裂纹萌生、扩展、贯通,直到宏观裂纹产生导致混凝土失稳断裂的过程。通过对数值模拟结果的分析,揭示出混凝土在拉伸条件下裂纹尖端的拉应力集中是裂纹扩展的动力,混凝土组成材料力学性质的非均匀性是造成裂纹扩展路径曲折的重要原因。     

考虑应力三轴度影响的30CrMnSiNi2A钢韧性断裂研究

30CrMnSiNi2A钢是一种在军工领域应用广泛的低合金高强度钢。针对结构完整性的评估问题,采用试验和数值计算结合的方法研究了30CrMnSiNi2A钢的韧性断裂特性。对光滑圆棒试件在不同温度下进行准静态和动态拉伸试验,并通过有限元迭代方法标定了材料的Johnson-Cook动态本构模型参数,分析了温度和应变率对30CrMnSiNi2A钢断裂行为的影响。开展了缺口圆棒拉伸、缺口平板剪切和圆柱压缩试验,计算了各试件对应的平均应力三轴度和断裂应变,给出了应力三轴度在?1/3～1.5区间内的断裂应变变化曲线,分别确定了Johnson-Cook和Bao-Wierzbicki失效模型参数。研究表明,30CrMnSiNi2A钢的断裂应变与应力状态密切相关,且在不同的应力三轴度区间内曲线单调性差异较大,Bao-Wierzbicki失效模型较好地描述了这种钢在不同应力状态下的断裂特性。     

Surface Residual Stress Measurement Using Curvature Interferometry

Surface roughness plays an important role in the delamination wear caused by rough surface contact. A recent dislocation model analysis predicts that nano-scale contacts of surface steps induce nucleation of dislocations leading to pro-load and anti-load dislocation segregation near the contact surface. Such dislocation segregation generates a sub-layer of tensile residual stress in a much thicker layer of compressive residual stress near the surface. The tensile sub-layer thickness is expected to be about 50 to 100 times the step height. In order to verify the predictions of the model analysis, contact experiments are carried out on polycrystalline aluminum surface to determine the existence of the tensile sub-layer. The variation of the residual stress along the thickness direction is measured using a newly developed high sensitivity curvature-measurement interferometer. The residual stress distribution measured with sub-nanometer spatial resolution indicates that contact loading leads to formation of a highly stressed sub-layer of tensile residual stress within a much thicker layer of compressive residual stress. Implications of tensile residual stress for delamination wear are discussed.     

Standard Uncertainty Evaluation for Dynamic Tensile Properties of Auto-Body Steel-Sheets

This paper is concerned with the standard uncertainty of the true stress–true strain curve as the tensile properties of auto-body steel sheets at intermediate strain rates ranged from 1 to 100 s^?1. A procedure to obtain true stress–true strain data is properly designed for the experiment and data acquisition. An analytic model is then established to evaluate the standard uncertainty of the measurand. The measurand in this case is the true stress which is a function of the input quantities: the tensile load; the initial length, the thickness and the width of a specimen; and the deformed length of a specimen. Sources of uncertainties of the input quantities are evaluated for the high speed tensile test with their associated sensitivity coefficients. Uncertainty of the stress data acquired is also considered in the procedure of the fast Fourier transform (FFT) smoothing process used to remove unnecessary signals acquired from experiments. Image analysis using a high speed camera is carried out to measure deformation of the specimen during high speed tensile tests with proper uncertainty evaluation. A combined standard uncertainty is evaluated from the uncertainties of the input quantities as well as the influence factor for the true stress of auto-body steel sheets at intermediate strain rates. Consequently, the true stress–true strain data are obtained with proper standard uncertainty evaluation.     

Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics (MD) simulations. An MD model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat Σ99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element—an atomistic analog to a continuum cohesive zone model element—the results from the MD simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion.     

Viscoelasticity and viscoplasticity of polypropylene/polyethylene blends

Observations are reported on polypropylene/polyethylene blends with various concentrations of components in uniaxial tensile tests with constant strain rates, relaxation tests, and creep tests at room temperature. A model is developed for the viscoelastic and viscoplastic responses of polymer blends at arbitrary three-dimensional deformation with small strains. Material constants in the constitutive equations are determined by fitting the experimental data. It is found that all adjustable parameters evolve with blend composition following an analog of the rule of mixture. Lifetime of blends under condition of creep rupture is evaluated by numerical simulation.     

A physical model for nucleation and early growth of voids in ductile materials under dynamic loading

Spall fracture and other rapid tensile failures in ductile materials are often dominated by the rapid growth of voids. Recent research on the mechanics of void growth clearly shows that void nucleation may be represented as a bifurcation phenomenon, wherein a void forms spontaneously followed by highly localized plastic flow around the new void. Although thermal, viscoplastic, and work hardening effects all play an essential role in the earliest stages of nucleation and growth, the flow becomes dominated by spherical radial inertia, which soon causes all voids to grow asymptotically at the same rate, regardless of differences in initial conditions or constitutive details, provided only that there is the same density of matrix material and the same excess loading history beyond the cavitation stress.These two facts, initiation by bifurcation at a cavitation stress, at which a void first appears, and rapid domination by inertia, are used to postulate a simple, but physically realistic, model for nucleation and early growth of voids in a ductile material under rapid tensile loading. A reasonable statistical distribution for the cavitation stress at various nucleation sites and a simple similarity solution for inertially dominated void growth permit a simple calculation of the initiation and early growth of porosity in the material.Parametric analyses are presented to show the effect that loading rate, peak loading stress, density of nucleation sites, physical properties of the material, etc. have on the applied pressure and distribution of void sizes when a critical porosity is reached.     

Non-linear creep damage under one-dimensional variable tensile stress

A non-linear damage relation, containing the axial strain history and a time integral over the stress history, is proposed for the case of one-dimensional time dependent tensile stress. Non-linear steady and transient creep terms are included in the axial strain relation, and elastic and creep Poisson's ratios are introduced into the lateral strain relation. Using these relations, complete damage solutions are obtained for the constant stress rate, step stress, relaxation and constant load tests. Observations are made concerning the associated rupture times.     

Numerical simulations of stress generation and evolution in Volmer–Weber thin films

We present a detailed model of the stresses and shape changes that occur in polycrystalline thin films during Volmer–Weber growth. Our model tracks the shape of an array of islands as they grow and coalesce into a continuous film. The islands change shape as a result of the deposition flux, as well as surface and grain boundary diffusion. Stress is generated in the film as a result of forces exerted between neighboring islands as they meet to form a grain boundary. The internal stresses in the islands and the diffusive changes on their surfaces and grain boundaries are computed using a coupled finite element scheme. Interactions between neighboring islands are modeled using a cohesive zone law. Our model predicts stress-thickness vs. thickness behavior that is in excellent agreement with experiments. Specifically, we observe a three-stage growth process consisting of a stress-free pre-coalescence stage, a rapid tensile rise at coalescence, and an eventual transition to a steady-state. The steady-state stress may be tensile or compressive, depending on the deposition rate, the grain size, and the properties of the film. Detailed parametric studies are conducted to establish the influence of material properties and growth conditions on the stress history, and the results are compared with experimental observations and previous models.     

微拉曼光谱研究M55JB碳纤维/微滴的拉伸变形行为

使用评价纤维/基体界面力学性能的新方法纤维微滴拉伸测试,来研究M55JB碳纤维/环氧树脂基体之间的界面应力传递性能。使用自制的微加载装置对碳纤维/环氧树脂微滴试样进行对称式拉伸测试,用微拉曼光谱仪记录下不同应变下的嵌入微滴内纤维上的拉曼频移信号,经过应力/频移关系转换成纤维轴向应力。实验结果显示,微滴内纤维轴向应力随载荷而明显增加。根据界面力平衡模型得到相应的界面剪切应力呈反对称式分布,在纤维嵌入端存在剪应力集中。新测试方法能保证嵌入微滴内纤维上的应力呈对称式分布,而且能降低纤维嵌入端附近的应力奇异性。     

Loss of adhesion at the tip of an interface crack

A model is constructed to analyze adhesive bond failure at the tip of an interface crack. The model is based on the assumption that there are zones of bounded cohesive tensile and shear stresses near a crack tip. Within the context of certain broad a-priori assumptions on the distributions of certain stress and displacement components in the cohesive zones, the requirement thatall stresses in the two materials remain bounded provides a method to compute the specific details for these zones. It is assumed that bond failure occurs when the extension of the bond fiber at the crack tip exceeds a critical value. For an interface crack in a uniform tension field computations for two alternate formulations suggest that this failure criterion is independent of the precise distribution of the cohesive stresses, but rather depends only upon their averaged values. Combined loading with a dominant tensile component has also been analyzed. If the critical extension of bond fibers and the maximum value of the cohesive tensile stress are known, the model provides the maximum allowable interface stresses for given crack dimension and material parameters.     

A variational approach to analyze a natural fault with hydraulic fracture based on the strain energy density criterion

A simplified analytical model of the interaction between a hydraulic fracture and an existing natural fault is developed. The mechanical activation of the natural fault as a result of contact with a pressurized fracture is described for plane strain conditions and quasi-static fracture propagation approximation. Using a variational approach, the normal and shear stresses, as well as the boundaries of the open and sliding zones along the fault, are predicted for three stages of the fracturing process (fracture approaching, coalescence, and fluid penetration). An accumulated concentration of shear stress at the tip of the fault’s sliding zone is shown to create sufficient tensile stress to initiate a new tensile crack on the opposite side of the fault, provided either the differential in situ stress is low or the friction coefficient is sufficiently large. The results of direct numerical simulation of the fracture interaction fit the model predictions made from the strain energy density fracture criterion.     

A method of three-dimensional strain measurement on non-ideal objects using holographic interferometry

Holographic interferometry has been applied to determine the components of tensile, compressive and shear strain in the surface layer of a non-ideal object subjected to high values of stress. The method consists of determining the three components of the vector displacement at a sufficient number of discrete points on the surface of the object. Functions in the form of truncated power series are fitted to the fringe order-distance data using the method of least squares. Interpolation of these functions is then carried out to obtain the fringe-order numbers at closely spaced equal intervals. The displacement in each interval is calculated and the displacement-distance relationship is then numerically differentiated to obtain strain. Components of stress at a particular point are then estimated by multiplying the strain value by the appropriate modulus. These stresses result from the application of considerable forces that are likely to cause large rigid-body displacements unless the object can be satisfactorily restrained. The difficulty of providing the required restraining forces has been avoided by mounting the object on a kinematic mount from which it can be removed before stressing and replaced afterwards. The accuracy of relocation of the object is sufficient to ensure the satisfactory formation of holographic interference fringes. As the use of the two-exposure holographic method results in a direction ambiguity of the displacement vector at any point of the surface, this method is complemented by electrical strain measurement. The strain is sampled in two convenient orthogonal directions at some part of the surface. The application of the uniqueness theorem of elasticity then permits the direction of displacement to be uniquely specified at any point of the surface. The electrical strain measurement also provides a check of the strain values determined by interferometry at various positions on the surface. This check is necessary since precise knowledge of the surface geometry of a non-ideal object may be lacking. Incorrect assumptions made about the geometry are shown to result in serious errors in the evaluation of strain. The method described has been used to estimate the stresses in the vicinity of a threaded hole in a sample of pipe for representative values of torque applied in screwing a connecting member into the pipe. Possible reasons for failure of the pipe in service are then deduced.     

Constitutive modeling of pressure dependent plasticity and fracture in solder joints

A new constitutive model describing the pressure dependence of plasticity and fracture in solder joints is proposed. The pressure dependence of the solders flow stress is obtained from the Peierls stress necessary to move mobile dislocations. Conservation of volume during plastic deformation is achieved through a deviatoric associated flow rule. Fracture is considered as a result of damage accumulation depending on the amount of plastic strain and triaxiality of stress the sample has experienced. The constitutive model was implemented in the FEM code Abaqus using the user subroutine UMAT. The model predictions were compared to experimental results of tensile tests performed with Sn-3.5Ag solder joints of various thicknesses. Ultimate tensile strength and ductility showed a strong dependency on the solder joints geometry. It is demonstrated that the model can nicely be fitted to experimental results.     

Hybrid experimental–numerical analysis of basic ductile fracture experiments for sheet metals

A basic ductile fracture testing program is carried out on specimens extracted from TRIP780 steel sheets including tensile specimens with a central hole and circular notches. In addition, equi-biaxial punch tests are performed. The surface strain fields are measured using two- and three-dimensional digital image correlation. Due to the localization of plastic deformation during the testing of the tensile specimens, finite element simulations are performed of each test to obtain the stress and strain histories at the material point where fracture initiates. Error estimates are made based on the differences between the predicted and measured local strains. The results from the testing of tensile specimens with a central hole as well as from punch tests show that equivalent strains of more than 0.8 can be achieved at approximately constant stress triaxialities to fracture of about 0.3 and 0.66, respectively. The error analysis demonstrates that both the equivalent plastic strain and the stress triaxiality are very sensitive to uncertainties in the experimental measurements and the numerical model assumptions. The results from computations with very fine solid element meshes agree well with the experiments when the strain hardening is identified from experiments up to very large strains.     

Residual-stress measurement using surface displacements around an indentation

An experimental method is described which can measure the direction and magnitude of residual and applied stress in metals. The method uses optical interference to measure the permanent surface deformation around a shallow spherical indentation in a polished area on the metal specimen. The deviation from circularly symmetrical surface deformations is measured at known values of applied stress in calibration specimens. This deviation from symmetry can then be used to determine the direction and magnitude of tensile residual stress in specimens of the same material. Determination of compressive residual stress is more limited. A model of the indentation process is offered which qualitatively describes experimental results in 4340 steel for both tensile and compressive stress. The model assumes that the deformation around an indentation os controlled by stresses analogous to those around a hole in an elastic plate. Various conditions are discussed which affect the indentation process and its use to measure stress, including (a) the rigidity of support of the indentor and specimen, (b) the size and depth of the indentation, (c) the uniaxial stress-strain behavior of the specimen material.