Relationship between tensile strength and porosity for foamed metals under equal speed biaxial tension

Abstract

A preliminary experimental investigation has been carried out on an isotropic three dimensional reticulated foamed metal with high porosity under biaxial tensile loading. The approximate relationship between tensile strength of these materials and their porosity has been evaluated under equal-speed biaxial tension loading. The mathematical formula is proved to be in a good agreement with the experimental data for nickel foam.     

On the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loading

In this paper, the modified Wöhler curve method proposed by Susmel and Lazzarin is employed to predict the fatigue life of welded connections subjected to biaxial cyclic loading. This criterion is reformulated here in order not to take into account the mean stress effect, as suggested by several design codes (at least when welded connections are not completely stress relieved). The accuracy of the proposed method in fatigue lifetime estimation was evaluated by using a number of data sets taken from the literature. The modified Wöhler curve method was applied in terms of nominal stresses and was calibrated using the uniaxial and torsional fatigue curve determined by reanalysing the experimental data, as well as using the standard fatigue curves of the Eurocode 3. The proposed approach was seen to be successful, giving multiaxial fatigue life predictions located within the widest scatter band related either to uniaxial or to torsional data, independently of both out‐of‐phase angle and load ratio value. Finally, the accuracy of the modified Wöhler curve method was compared to the one obtained by applying the procedure suggested by the Eurocode 3: the proposed criterion is demonstrated to be much more accurate and reliable than the standard one.     

A new analytical method for stress intensity factors based on insitu measurement of crack deformation under biaxial tension

A new approach for the calculation of stress intensity factors (SIF) for isotropic and orthotropic materials under biaxial tension loading was proposed in this paper. In order to determine SIF from the full-field displacement data, an asymptotic expansion of the crack tip displacement field was performed. The deforming shape and surface residual stress of the crack tip was obtained at the early extended stage of the loading process by using optical microscope and X-ray diffraction measurement. During this stage, a modified Dugdale Model, which takes into account the coupled effect at the crack tip, was proposed for the open displacement of the crack tip. In this paper, the SIFs of two types of silicon steel sheet with isotropic and orthotropic properties were calculated using the modified Dugdale Model based on the biaxial tension experimental data. From the results, it was found that analysis using the modified Dugdale Model is an effective way to evaluate SIF under biaxial stress.     

A continuum elastic–plastic model for woven-fabric/polymer-matrix composite materials under biaxial stresses

In this study a simple continuum model for the macro-mechanical prediction of the elastic–plastic behavior of woven-fabric/polymer-matrix composites has been proposed. This model uses a scalar hardening parameter (which is a function of the current applied stress state) instead of an effective stress-strain relation to determine plastic strain increments. For simplicity, the stresses are expressed as invariants based on the material symmetry. It has been shown, by the use of experimental data for two different woven-fabric/polymer-matrix composite materials, that the newly proposed model accurately describes the non-linear mechanical behavior for different in-plane biaxial stress states ranging from pure shear to pure tension.     

A structural constitutive model for chemically treated planar tissues under biaxial loading

Chemically treated, biologically derived soft collagenous tissues are used extensively in medical devices. To enable prosthesis design through computational methods, physically realistic constitutive models are required. In the present study, a structural approach was utilized that incorporated experimentally measured angular distribution of collagen fibers. Using biaxial mechanical data from our previous study (Annals of Biomedical Engineering, vol. 26(5), pp. 892–902, 1998), the effective fiber and matrix stress–strain responses were predicted. The agreement with the experimental data supported the assumption that the mechanical effects of chemical treatment are equivalent to the addition of an isotropic elastic matrix. An important utility of this model is its ability to separate the effects of chemical treatment on the fibers and matrix. Applications of this approach include utilization in the design of novel chemical treatments that produce specific mechanical responses, the study of fatigue damage, and finite element implementation for tissue engineering scaffold design. Received 4 November 1999     

A new multiaxial fatigue damage model for various metallic materials under the combination of tension and torsion loadings

Based on the critical plane approach, a new damage parameter for multiaxial fatigue damage is presented. Both components of strain and stress are considered in this parameter. Thus, a new multiaxial fatigue damage model is given based on the critical plane approach. The capability of fatigue life prediction for the proposed fatigue damage model is checked against the experimental data of Hot-rolled 45 Steel, S460N Steel, 1045HR Steel, 30CrMnSiNi2A alloy steel, and GH4169 alloy at elevated temperature, and the predicted results are compared with results from common multiaxial fatigue model. It is demonstrated that the proposed criterion gives better satisfactory results for all the five checked materials.     

Effect of thermal residual stresses on matrix failure under transverse tension at micromechanical level: A numerical and experimental analysis

In the present work the influence at micromechanical scale of thermal residual stresses, originated in the cooling down associated to the curing process of fibrous composites, on inter-fibre failure under transverse tension is studied. In particular, the effect of the presence of thermal residual stresses on the appearance of the first debonds is discussed analytically, whereas later steps of the mechanism of damage, i.e. the growth of interface cracks and their kinking towards the matrix, are analysed by means of a single fibre model and making use of the Boundary Element Method (BEM). The results are evaluated applying Interfacial Fracture Mechanics concepts. The conclusions obtained predict, at least in the case of dilute fibre packing, a protective effect of thermal residual stresses against failure initiation, the morphology of the damage not being significantly affected in comparison with the case in which these stresses are not considered. Experimental tests are carried out, the results agreeing with the conclusions of the numerical analysis.     

Phenomenological rheological model and the criterion of failure of metals under uniaxial stress

The article suggests an energy alternative of the phenomenological rheological equations and criteria of failure of metals for a broad range of stresses including stresses higher than yield stress. The approach is based on the hypothesis that the damage to material is proportional to the linear combination of the work of true stress on creep strain and plastic strain. From the same positions the article describes the nonmonotonic nature of the curve of elastoplastic strain, the nonlinear nature of the curve of creep limit, it identifies the stage of avalanche creep, etc. The model was experimentally checked on the alloy ÉP742 at 650 and 750°C. Agreement between theoretical and experimental data was obtained.Translated from Problemy Prochnosti, No. 11, pp. 13–19, November, 1991.     

A new plasticity and failure model for ballistic application

Ballistic phenomena give rise to a plethora of failure modes that compete. Johnson–Cook (JC) plasticity and failure models have been extremely successful because, while being conceptually simple, they capture the essence of the operative mechanics and they provide reasonably good predictions for ballistic limits. Nevertheless, the Johnson–Cook models, due to their isotropic flow and failure surface, cannot reproduce certain failure modes commonly seen in quasistatic tests: cup and cone failure, slanted failure in tensile specimens, and slanted failure in compression specimens. This work shows that by introducing the third invariant (or Lode angle) in both the JC plasticity and damage models, cup and cone, and slanted failure modes arise naturally. After the model is presented it is exercised with a material taken from the literature to predict successfully Taylor anvil and ballistic penetration failure patterns.     

Analysis of brittle fracture under the combined stresses of tension and compression

Brittle fractures occurring under biaxial stress states were analysed based on the weakest link model using the mixed mode fracture criterion. Expressions for the mixed mode fracture criterion were chosen for application to the negativeK _l region, corresponding to the compressive stress for the crack. Calculations for biaxial strength with randomly oriented constant-length cracks from the mixed mode fracture criterion were made in the region ofK _I>0 because an unstable fracture seems to occur in this region. The results indicated that the tensile stress component in the combined tension and compression stress state remains constant when the compressive component is smaller than the critical value, which is given by [1 –(K _c/K _c)²]_t derived from the mixed mode fracture criterion, (K /K _c) + (K /K _c)² = 1. Considering the statistical effects, however, calculation of the biaxial strength is modified to result in: (1) lowering the biaxial tensile strength, and in (2) a smooth transition from the constant tensile strength region to the decreasing strength region under the combined tension and compression stress. This suggests that the highK _IIc/K_Ic ratio results in the increase in the compressive strength relative to the tensile strength.     

A model for foamed cementing of oil and gas wells

We present a two-dimensional model of the primary cementing process for foamed cement slurries. Foamed cement slurries have a number of claimed advantages, but also have a pressure-dependent density and rheology. The rheology is hard to quantify fully over all ranges of foam quality, which compromises the accuracy of models. The density variation is due to expansion/compression of the gas phase along the well, caused by variations in the static pressure. We show that in the absence of careful control, buoyancy-driven instabilities can result in the annulus, as the foamed slurry expands and the density drops below that of the displaced drilling mud. These instabilities appear to be of a classic porous media/Hele-Shaw cell fingering type, triggered by a threshold unstable density difference. We show that these instabilities are amplified by wellbore eccentricity, occurring lower in the well than in a concentric annulus. Our results question the safe usage of foamed cements in primary cementing.     

A new failure criterion for the Gurson-Tvergaard dilational constitutive model

In the Gurson-Tvergaard model a failure criterion has to be used to signify the void coalescence. In the literature, a constant critical void volume fraction criterion has been widely used. However, it is questionable whether the critical void volume fraction is a material constant and, furthermore, it is also difficult in practice to determine the constant. By modifying Thomason's plastic limit-load model, a new failure criterion which is fully compatible with the Gurson-Tvergaard model, is presented in this study. In the present criterion, the void coalescence failure mechanism by internal necking has been considered and the material failure is a natural result of the development of dual constitutive, stable and unstable, responses. In practical application of the present criterion, no critical void volume fraction needs to be pre-determined either numerically or experimentally. Furthermore, according to the new criterion, the void volume fraction corresponding to void coalescence is not a material constant, rather a function of stress triaxiality. The predictions using the present criterion have been compared with the finite element results by Koplik and Needleman, and very good agreement is observed. The potential advantage of this criterion and other related issues are discussed.     

A compact analytical material model for unconfined concrete under uni-axial compression

The majority of the published material models for unconfined concrete under uni-axial compression consist of two branches. The recent trend is to introduce empirical modification factors in the existing material models to improve agreement between experimental and analytical results, particularly for High Strength Concrete. This paper presents a compact analytical material model in which the available conditions uniquely determine all the model parameters. It consists of a single branch and the need for empirical factors is eliminated. An application of this material model to published experimental data on normal and lightweight concretes over a wide strength range demonstrates its versatility. The agreement between experimental and analytical results is as good as that which may be provided by any other existing model. The rationality and elimination of empiricism are additional gains.

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Résumé La majorité de modèles de matériaux publiés pour du béton non confiné sous compression uni-axiale sont constitués de deux parties. Une tendance récente est d'introduire des facteurs de modification empiriques dans les modèles de matériaux existants afin d'améliorer la concordance entre les résultats expérimentaux et analytiques, en particulier pour le béton à hautes performances. Cette étude présente un modèle de matériau compact et analytique dans lequel les conditions disponibles déterminent d'une manière unique tous les paramètres du modèle. Il est constitué d'une seule partie et les facteurs empiriques ne sont plus nécessaires. Une application de ce modèle de matériau à des données expérimentales publiées sur des bétons ordinaires et légers pour une large gamme de résistances démontre sa souplesse. La concordance entre les résultats expérimentaux et analytiques est aussi bonne que celle que peut fournir un autre modèle existant. La rationalité et l'élimination de l'empirisme sont des avantages additionnels.

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A new variant for measuring the surface tension of liquid metals and alloys by the oscillating drop method

The theoretical background of the oscillating drop technique for measuring surface tension is briefly presented and the different analysis procedures are cited. A new method is described for obtaining oscillation frequencies by fast fourier transformation (FFT) of the pyrometer voltage signals from temperature measurements at the top of the levitated sample. The results on the first experiments on liquid nickel are in a good agreement with the hterature data.Paper presented at the Fourth International Workshop on Subsecond Thermophysics. June 27–29, 1995, Köln, Germany.     

A continuum damage mechanics model with the strain-based approach to biaxial low cycle fatigue failure

A continuum damage mechanics model for low cycle fatigue failure of initially isotropic materials under biaxial loading conditions is presented. The expression for the equivalent strain in the fatigue damage evolution equation contains the three material parameters, and the strain intensity as well as the maximum principal strain and the volume strain for amplitudes. It is shown how these material parameters can be determined from a series of basic experiments using a cruciform specimen. Particular expressions for the equivalent strain with a smaller number of material parameters and invariants are obtained. Model predictions are found to be in satisfactory agreement with the experimental low cycle fatigue data under full ranged biaxial loadings obtained in the test using a cruciform specimen.     

Validity limits of the Dugdale model for thin cracked plates under biaxial loading

Experimental results show that there are significant biaxial effects on the fracture behaviour of thin cracked plates. In this paper we examine the possibility of extending the Dugdale model in the presence of biaxial loads. This investigation is mainly concerned with the validity limits of the model in respect of the plastic flow rules. Through a careful analysis of the correspondence between applied and local stresses, it is shown that the Dugdale model fails when the applied stress parallel to the crack plane is higher than the applied stress normal to it. In this case the flow rules are significantly violated.