Yield behavior of porous nuclear fuel (UO2)

Uranium dioxide (UO₂) is one of the most common nuclear fuels. During burn-up, the fuel undergoes substantial microstructural changes including the formation of pressurized pores, thus becoming a porous material. These pores reduce the elastic modulus and alter the yield behavior of the material. In this work, a finite-element-based homogenization technique has been used to map the yield surface of UO₂ with pressurized pores. Two scenarios are considered; in the first, the fuel matrix is a ductile material with a Von-mises type behavior, while in the second, the matrix is quasi brittle, which is simulated using the concrete damaged plasticity (CDP) model available in ABAQUS. For both of the scenarios, it is found that the yield strength decreases with an increase in porosity for a given internal pore pressure. For a given porosity, the yield surface shifts towards the negative hydrostatic axis in the Haigh-Westergard stress space with an increase in pore pressure. When the matrix is quasi brittle, the decrease in tensile hydrostatic strength is less than the increase in compressive hydrostatic strength, whereas in the case of a ductile matrix, the changes in the hydrostatic strengths are same. Furthermore, the shape of the yield surface changes from one deviatoric plane to another in both scenarios. Analytical equations, which are functions of pore pressure and porosity, are developed to describe the yield surface of porous UO₂ while accounting for the changes in shape of the yield surface from one deviatoric plane to another. These yield functions can be used to predict the failure of porous UO₂ fuel.     

Material parameters for pressure-dependent yielding of unidirectional fiber-reinforced polymeric composites

We study elasto-plastic deformations of unidirectional fiber reinforced polymeric composites (UFPCs) with fibers assumed to deform elastically and the matrix elasto-plastically. The matrix’s and hence composite’s plastic deformations are analyzed by using both the pressure-independent von Mises yield surface and the pressure-dependent Drucker–Prager yield surface and the associated flow rules. In both cases the strain hardening of the matrix is considered and values of material parameters for the matrix are obtained by computing the effective stress versus the effective plastic strain curves from experimental uniaxial stress–strain curves. Values of parameters in the yield surface for the UFPC in terms of those of the matrix and the volume fraction of fibers are found by using a micromechanics approach. Wherever possible, the computed results are compared with the corresponding experimental findings available in the literature. Significant contributions of the work include providing a methodology for determining values of elasto-plastic material parameters for a UFPC from those of its constituents and their volume fractions, and giving expressions in terms of volume fractions of fibers for material parameters appearing in the yield surface of the composite.     

Deformation mechanisms and the yield surface of low-density,closed-cell polymer foams

The geometry of low-density, closed-cell, polyethylene and polystyrene foams was modelled with a Kelvin foam having uniform-thickness cell faces; finite element analysis (FEA) considered interactions between cell pressures and face deformation. Periodic boundary conditions were applied to a small representative volume element. In uniaxial, biaxial and triaxial tensile stress states, the dominant high-strain deformation mechanism was predicted to be tensile yield across nearly flat faces. In uniaxial and biaxial compression stress states, pairs of parallel plastic hinges were predicted to form across some faces, allowing them to concertina. In hydrostatic compression, face bowing was predicted. The rate of post-yield hardening changed if new deformation mechanisms became active as the foam strain increased. The effects of foam density and polymer type on the foam yield surface were investigated. Improvements were suggested for foam material models in the FEA package ABAQUS.     

Effect of strain rate on the tension–compression asymmetric responses of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si

An experimental investigation is performed to explore the tension–compression asymmetry of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si alloy over a wide range of strain rates. A split Hopkinson bar technique is used to obtain the dynamic stress–strain responses under uniaxial tension and compression loading conditions. Experimental results indicate that the alloy is a rate sensitive material. Both tension yield strength and compression yield strength increase with increasing strain rate. The mechanical responses of the alloy have the tension–compression asymmetry. The values of yield strength and subsequent flow stress in compression are much higher than that in tension. The yield strength is more sensitive to change with strain rate in tension than compression. The difference of the yield strength between tension and compression increases with the increase of strain rate. The tensile specimen is broken in a manner of ductile fracture presenting characteristic dimples, while the compressive specimen fails in a manner of localized shearing failure.     

The multiaxial yield behaviour of an aluminium alloy foam

The multi-axial yield behaviour of the aluminium alloy foam Alulight has been measured. Triaxial tests have been performed on a range of relative densities in order to compare the hydrostatic stress versus strain response with the uniaxial compressive response, and to probe the yield surface after prior hydrostatic compression. It is found that the degree of strain hardening in hydrostatic compression exceeds that for uniaxial compression, and the yield surface remains almost self-similar in shape after hydrostatic compaction. The measured yield surface provides support for the phenomenological yield model of Deshpande and Fleck (V. S. Deshpande, N. A. Fleck, Journal of Mechanics and Physics of Solids, 48, (2000), 1253). Upon reviewing the available experimental evidence from this and previous studies it is found that a broad correlation emerges between the relative density and the shape of the yield surface for metallic foams.     

Mechanical experiments on the superplastic material ALNOVI-1, including leak information

In subatomic particle physics, unstable particles can be detected with a so-called vertex detector, placed inside a particle accelerator. A detecting unit close to the accelerator bunch of charged particles must be separated from the accelerator vacuum. A thin sheet with a complex 3D shape prevents the detector vacuum from polluting the accelerator vacuum. Therefore, this sheet has to be completely leak tight. However, this can conflict with restrictions concerning maximum sheet thickness of the product. To produce such a complex thin sheet, superplastic forming can be very attractive in cases where a small number of products is needed. In order to predict gas permeability of these formed sheets, many mechanical experiments are necessary, where the gas leak has to be measured. To obtain insight in the mechanical behaviour of the used material, ALNOVI-1, tensile experiments were performed to describe the uniaxial stress-strain behaviour. From these experiments, a high strain rate sensitivity was measured. The flow stress of this material under superplastic conditions was low and the material behaved in an isotropic manner upon large plastic strains. The results of these experiments were used to predict the forming pressure as a function of time in a free bulge experiment, such that a predefined target strain rate will not be exceeded in the material. An extra parameter within these bulging experiments is the application of a hydrostatic pressure during the forming process. Such a pressure postpones the nucleation and growth of internal cavities, which means that higher plastic strains can be reached before failure. Results from these experiments showed that at higher hydrostatic pressures, higher bulges were made. All these bulges were leak tested, showing also that higher hydrostatic pressures lead to a lower void volume fraction at higher hydrostatic pressures, since these bulges were more leak tight at the same bulge height than bulges made without the application of this pressure. This article describes the setup and results of the uniaxial (tensile) and biaxial (bulging) experiments on the superplastic aluminium ALNOVI-1.     

More on the effects of thermal residual and hydrostatic stresses on yielding behavior of unidirectional composites

The influence of manufacturing process thermal residual stresses and hydrostatic stresses on yielding behavior of unidirectional fiber reinforced composites has been investigated when subsequently subjected to various mechanical loadings. Three-dimensional finite element micro-mechanical models have been used. The results of this study reveal that the size of the initial yield surface is highly affected by the thermal residual and hydrostatic stresses. It was also found that effects of a uniform temperature change on the initial yield surface in the composite stress space is not equivalent to a solid translation of the surface in the direction of the hydrostatic stress axis. At the micro-level, magnitudes of various stress components within the matrix due to the thermal residual and hydrostatic stresses are different. However, at a macro-level, both temperature change and hydrostatic loading of composites show similar effects on the initial yield surface in the composite stress space. In an agreement with experimental data, results also show that residual stresses are responsible for asymmetric behavior of composites in uniaxial tension/compression in the fiber direction. This asymmetric behavior suggests that the existing quadratic yield criteria need modification to include thermal residual stress effects.     

Three-dimensional creep measurements in young concrete

Creep tests are reported in which sealed concrete specimens were loaded at the early age of 1 day and maintained under load for a further 61 days. Three systems of compressive stress were applied, uniaxial, equal biaxial and hydrostatic, all principal stresses being less than 50 percent of the uniaxial strength. It was found that Poisson's ratio for total strain (elastic+creep) remained sensibly constant throughout the test and was little affected by the system of loading. In general, the characteristics of creep and creep recovery under the multiaxial stress systems are the same as those observed in older concrete. A further test with stresses of 70–100 percent of the uniaxial strength resulted in increased unit strains, even under hydrostatic stress.     

Evolution of mechanical properties for a dual-phase steel subjected to different loading paths

The evolution of the mechanical properties of a dual-phase (DP590) steel sheet after being prestrained by uniaxial tension, plane strain and equal biaxial stretching was investigated. Specimens were first loaded using the three prestraining modes. Then, from the prestrained specimens, a few sub-sized samples were machined along the rolling direction and the transverse direction for further uniaxial tension testing. Six loading paths were provided. Equal biaxial stretching was performed using a cruciform specimen. The evolution of work hardening performance, elastic modulus, yield stress and tensile stress under the six loading paths were discussed in detail. The results indicate that loading paths can affect the latent work hardening performances, strain hardenability, yield stress and tensile stress evolution as well as the elastic modulus decrease during plastic deformation. The uniaxial tension–uniaxial tension path results in a cross-softening phenomenon, the largest yield stress enhancement and a mild maximum tensile stress increase. The equal biaxial stretching-uniaxial tension path leads to a cross-hardening phenomenon, the least yield stress enhancement and the largest tensile strength increase maximum tensile strength. The elastic modulus of DP590 steel not only changes with the accumulated plastic strain but also varies with the loading paths. The largest decrease of the elastic modulus equal biaxial stretching–uniaxial tension can reach 12.7% beyond 8% equivalent strain, which is 5.2% greater than that in the monotonic uniaxial tension path.     

Modeling the inelastic deformation and fracture of polymer composites – Part I: Plasticity model

A new transversely-isotropic elastic–plastic constitutive model for unidirectional fiber reinforced polymers (FRP) is presented. The model is able to represent the fully nonlinear mechanical behavior under multi-axial loading conditions and under triaxial stress states prior to the onset of cracking. Since associated flow rules often give a wrong prediction of plastic Poisson coefficients, a non-associated flow rule is introduced to provide realistic predictions of the volumetric plastic strains. This paper focusses on the simulation of triaxiality dependent plasticity based nonlinearities of FRP until failure occurs. The onset and propagation of failure is predicted by a new smeared crack model presented in an accompanying paper (Camanho et al., 2012). In order to demonstrate the capabilities of the new material model, a yield surface parameter identification for IM7-8552 carbon epoxy is presented and simulations of quasi-static transverse and off-axis compression tests and of uniaxial compression tests superimposed with various values of hydrostatic pressure are shown as a model verification.     

Strength and stress–strain characteristics of traditional adobe block and masonry

Traditional unstabilized adobe low-rise buildings are common in many Chinese small towns and villages. This paper presents a study on the uniaxial compressive strength and stress–strain behavior of traditional unstabilized adobe blocks and masonry prisms with various compositions. The adobe blocks were manually produced by Chinese traditional technique in various proportions of natural soil and sand. The influence of various proportions on unconfined compressive strength, dry density and initial tangent modulus are discussed. Following this, soil mortars in three different proportions were used to construct adobe masonry prisms, with the purposes of understanding the influence of mortar strength to block strength ratio on compressive strength and stress–strain characteristics. The result shows that the compressive strength, initial tangent modulus and Poisson’s ratio of prism are influenced by the ratio of mortar strength to block strength. In addition, tangent modulus and Poisson’s ratio increase with the ratio of stress to peak strength. It was also found that although coefficients of variation of experimental results are reduced by load–unload cycles, peak strains are largely increased.     

Numerical implementation of a J_2- and J_3-dependent plasticity model based on a spectral decomposition of the stress deviator

A new plasticity model with a yield criterion that depends on the second and third invariants of the stress deviator is proposed. The model is intended to bridge the gap between von Mises’ and Tresca’s yield criteria. An associative flow rule is employed. The proposed model contains one new non-dimensional key material parameter, that quantifies the relative difference in yield strength between uniaxial tension and pure shear. The yield surface is smooth and convex. Material strain hardening can be ascertained by a standard uniaxial tensile test, whereas the new material parameter can be determined by a test in pure shear. A fully implicit backward Euler method is developed and presented for the integration of stresses with a tangent operator consistent with the stress updating scheme. The stress updating method utilizes a spectral decomposition of the deviatoric stress tensor, which leads to a stable and robust updating scheme for a yield surface that exhibits strong and rapidly changing curvature in the synoptic plane. The proposed constitutive theory is implemented in a finite element program, and the influence of the new material parameter is demonstrated in two numerical examples.     

Computational coupling of moisture diffusion and mechanical deformation in polymer matrix composites

A computationally efficient multiscale–multiphysics model aimed at predicting mechanical response of thermoplastic composites subjected to different levels of moisture was developed. The mathematical model of the coupled moisture‐diffusion–mechanical‐deformation phenomenon was stated at the microscale, based on the observed experimental data, and then upscaled using a mathematical homogenization approach. A two‐way coupling between moisture diffusion and mechanical deformation was introduced by which diffusivity was enhanced by hydrostatic strain, whereas strength and stiffness were assumed to degrade because of moisture ingression, which also gives rise to swelling. The computational complexity of analyzing the two coupled physical processes at multiple scales was reduced via a model reduction scheme for multiple physical processes. The model was validated for 30% by weight filled glass fiber and carbon fiber reinforced thermoplastic composites. The moisture conditioning and uniaxial tension experiments were utilized to identify diffusion and mechanical properties at a fine scale. The identified properties were then used to validate the formulation in the three‐point bending test. Copyright © 2014 John Wiley & Sons, Ltd.     

Effect of notch root radius on tensile behaviour of 316L(N) stainless steel

Abstract

Type 316L(N) stainless steel (SS) is used as the major structural material for high temperature components of sodium cooled fast reactors. The influence of notch root radius on the tensile behaviour of 316L(N) SS under multi-axial stress state was investigated. Double U-notches with five different kinds of notch geometry were incorporated symmetrically into the tensile testing specimens by changing the notch root radius while keeping the gross diameter, net diameter and notch depth as the same for all the notches. The notch root radius was varied as 0·25, 0·5, 1·25, 2·5 and 5 mm. Tensile tests were carried out on the notched specimens at room temperature (298 K) and at 923 K at a constant strain rate of 3×10^?3 s^?1. The tensile strength and yield strength of notched specimen of 316L(N) SS increased with decrease in notch radius at both the temperatures and the notch severity was less pronounced at high temperature. The fractured notch surface was analysed using scanning electron microscope and unfractured notch was sliced along the axis and observed under optical microscope. Finite element analysis was performed on the models of notched specimens with various notch root radii. These results showed that Von Mises equivalent stress which was derived from triaxial stresses decreased with decrease in notch radius. The shift of location of peak values of maximum principal stress and hydrostatic stress towards the axis of the specimen, leading to formation of cracks, occurred at a lower nominal stress when the notch radius was increased.     

Three-parameter yield criterion for a brittle polyester resin

The tensile and compressive strengths of three polyester resins were measured under superposed hydrostatic pressure extending to 300 MPa, in an attempt to establish yield criteria. The polyesters were brittle in uniaxial tension at all pressures, and accordingly, a third testing geometry, diametral compression of a disc, was employed to complete the two or three necessary parameters to establish the yield surface in stress space. From the biaxial (disc) and axial compressive test data, the atmospheric tensile yield strength (higher than the fracture strength) was computed to be ～67 MPa in comparison with the compressive strength of ～120 MPa, their ratio 0.56 being significantly less than the more common 0.75 found for thermoplastics and epoxides. The data for compressive yield strength under superposed pressure were compared with the predictions of the two-parameter pyramidal, conical and paraboloidal criteria and the fit, though reasonable for the latter, could be significantly improved if a further independent material parameter was employed to give a three-parameter pyramidal criterion (the principal stresses σ₁, σ₂ and σ₃ being measured in MPa) of the form 0.0150σ₁?0.0039σ₂?0.0083σ₃=1     

岩样单轴压缩峰后泊松比理论研究

研究了单轴压缩岩样应变软化阶段侧向应变与轴向应变的比值(峰后泊松比)的变化规律.岩样的塑性变形假设根源于塑性应变局部化.岩样的轴向及侧向变形被分别分为两部分:弹性变形(由虎克定律描述)及由局部化引起的塑性变形(由梯度塑性理论及几何关系确定).应变软化阶段的轴向应变-侧向应变曲线、轴向应力-轴向应变曲线及轴向应力-侧向应变曲线都得到了实验验证.在峰值强度时,峰后泊松比等于峰前泊松比.当压缩应力降至零时,峰后泊松比达到临界值.该临界值可能比峰前泊松比大,也可能比它小.峰后泊松比还和试件尺寸有关,这与峰前泊松不同.峰后泊松比与轴向压应力之间的关系可能是一条直线,也可能是上凸的,或上凹的.这取决于岩石的本构参数(弹性模量、剪切及软化模量、剪切带宽度及峰前泊松比)、试件的结构尺寸(试件宽度及高度)及剪切带倾角之间的关系.     

EVOLUTION OF TRANSVERSE MATRIX CRACKING IN CROSS-PLY LAMINATES

The objective of this paper is to develop a micromechanics model for the onset and subsequent multiplication of transverse cracks in the 90° layers of a cross-ply laminate under uniaxial tension. The micromechanics study of transverse matrix cracking is performed by a combination of finite element and analytical analyses. Based on the Griffith fracture criterion, the evolution of transverse matrix crack density is predicted. The prediction compares well with existing experimental data in the literature. Analytical expressions of the non-linear effective stress–strain curves are also obtained for a wide range of material systems. In addition, an analytical expression of the effective stiffness is derived based on the differential self-consistent method. The analytical results agree very well with the finite element calculations.     

Crack tip displacements of microstructurally small surface cracks in single phase ductile polycrystals

A planar double slip crystal plasticity model is applied to the evaluation of crack tip opening (CTOD) and sliding (CTSD) displacements for microstructurally small stationary cracks under monotonic loading for a material with nominal stress-strain behavior that is representative of a relatively high strength helicopter rotor hub material. Two-dimensional plane strain finite element calculations are presented for CTSD and CTOD of microstructurally small transgranular surface cracks in a polycrystal subjected to monotonic loading. The effects of crack length relative to grain size, orientation distribution of nearest neighbor grains, stress state and stress level are considered for nominal stress levels below the macroscopic yield strength. The CTOD and CTSD are computed for stationary crystallographic surface cracks with various realizations of crystallographic orientations of surrounding grains. It is found that (i) the opening displacement is dominant for remote tension even for crystallographic cracks oriented along the maximum shear plane in the first surface grain, (ii) there is a strong dependence of the CTOD on the proximity to grain boundaries, but lesser dependence of the CTSD, and (iii) that the elastic solutions for CTOD and CTSD are valid below about 30% of the 0.2% offset-defined yield strength.     

油气输送管典型应力状态下的屈服行为研究

准确计算油气输送管的实际屈服强度对合理确定输送压力有重要影响。该文分析了4种应力状态下对屈服强度有明显影响的钢管轴向应力,发现管材横向小试样试验时,轴向应力为零,工厂静水压试验时,轴向应力小于零,裸露钢管静水压试验时,轴向应力为环向应力的一半,埋地服役状态时,轴向应力为0.3倍环向应力。并从理论和试验两方面分析了实物钢管屈服强度与管材小试样屈服强度的差别。理论计算表明,4种应力状态下,屈服时vonMises理论计算的钢管环向应力值大于或等于Tresca理论计算值,其中裸露钢管受内压状态下,vonMises理论计算的管道屈服环向应力为1.15倍管材屈服强度,Tresca理论计算值为1.0倍,6根钢管爆破试验及小试样拉伸试验表明,该值为1.18倍。vonMises理论比Tresca理论更适合油气输送管的屈服计算。     

Effect of strain gradients on the size effect of concrete in uniaxial tension

A series of uniaxial tension experiments has been conducted to investigate the size effect on strength and fracture energy of quasi brittle materials like concrete and sandstone. This paper focuses on the results of the concrete tests, and specifically deals with the variation of the nominal strength for specimens of six different sizes in a scale range of 1:32. It was found that under given experimental conditions, the nominal strength strongly depended on the specimen size. More important however, is the fact that most of this size effect could be attributed to strain gradients which were present in the cross section of the specimens. These strain gradients were caused by the specimen shape, load eccentricity and material inhomogeneity. Through a combination of experimental data and a simple linear elastic analysis, the importance of strain gradients with respect to the ultimate load level could be visualized. This leads to the conclusion that studying a material size effect is not possible without taking into account structural stress/strain gradients. This revised version was published online in July 2006 with corrections to the Cover Date.