Fracture energy of epoxy resin under plane strain conditions

The fracture behaviour of an epoxy resin has been studied by a method which involves the pressurization of an internal circular crack. The method can be used to study both cohesive fracture and the adhesive failure of an interface. Plane strain conditions are assured because the crack does not intersect a free surface and (for adhesive failure) shrinkage stresses are eliminated as a crack driving force. Using high speed photography, the dependence of crack speed on critical pressure and specimen geometry was determined. An elastic analysis permits the derivation of fracture energy as a function of crack velocity. Fracture energy values lay between 100 and 200 Jm^–3 at 35° C with a peak at a crack velocity of 37 m sec^–1.     

Dynamic shear band development in plane strain compression of a viscoplastic body containing a rigid inclusion

Summary We study the plane strain thermomechanical deformations of a viscoplastic body containing a rigid non-heat-conducting ellipsoidal inclusion at the center. Two different problems, one in which the major axis of the inclusion is parallel to the axis of compression and the other in which it is perpendicular to the loading axis are considered. In each case the deformations are presumed to be symmetric about the two centroidal axes and consequently deformations of a quarter of the block are analyzed. The material of the block is assumed to exhibit strain-rate hardening, but thermal softening. The applied load is such as to cause deformations of the block at an overall strain-rate of 5000 sec^–1. The rigid inclusion simulates the presence of second phase particles such as oxides or carbides in a steel and acts as a nucleus for the shear band.It is found that a shear band initiates near the tip of the inclusion and propagates along a line inclined at 45° to the horizontal axis. At a nominal strain of 0.25, the peak temperature rise near the tip of the vertically aligned inclusion equals 75% of that for the horizontally placed inclusion. The precipitous drop in the effective stress near the inclusion tip is followed somewhat later by a rapid rise in the maximum principal logarithmic strain there.     

Simulating interaction of two symmetric grain boundaries under shear strain conditions

The behavior of two large-angle grain boundaries of the Σ = 5 (210)[001] special type in a copper polycrystal under shear loading conditions has been numerically simulated. It is established that, similar to the case of a single boundary of this type, the grain boundaries shifts in the direction perpendicular to that of shear straining simultaneously with the relative slippage of grains in the direction of applied load. Features of the interaction of two symmetric defects that approach each other are considered. The obtained results provide a better understanding of the atomic mechanisms of plastic strain development in polycrystalline materials.     

Quartz resonator instabilities under cryogenic conditions

The phase noise of a quartz crystal resonator working at liquid helium temperatures is studied. Measurement methods and the device environment are explained. The phase noise is measured for different resonance modes, excitation levels, amount of operating time, device orientations in relation to the cryocooler vibration axis, and temperatures. Stability limits of a frequency source based on such devices are evaluated in the present measurement conditions. The sources of phase flicker and white noises are identified. Finally, the results are compared with previous works.     

A numerical study of plasticity induced crack closure under plane strain conditions

The level of plasticity induced crack closure (PICC) is greatly affected by stress state. Under plane strain conditions, however, the level and even the existence of PICC still are controversial. The objective here is to study the influence of the main numerical parameters on plane strain PICC, namely the total crack propagation, the number of load cycles between crack increments, the finite element mesh and the parameter used to quantify PICC. The PICC predictions were included in a parallel numerical study of crack propagation, in order to quantify the impact of plane strain values on fatigue life. The results indicate that literature may be overestimating plane strain PICC due to incorrect numerical parameters. The number of load cycles usually considered is unrealistically small, and its increase was found to vanish crack closure, particularly for kinematic hardening. This effect was linked to the ratcheting effect observed at the crack tip. The total crack increment, Δa, must be large enough to obtain stabilized PICC values, but this may imply a huge numerical effort particularly for 3D models. The size of crack tip plastic zone may be overestimated in literature, which means that the meshes used may be too large. Additionally, the crack propagation study showed that the plane strain PICC has usually a dominant effect on fatigue life, and plane stress PICC is only relevant for relatively thin geometries.     

The effect of work-hardening on plane strain crack growth under small scale yielding conditions

Though highly idealized in character, the Dugdale-Bilby-Cottrell-Swinden (DBCS) line plastic zone model, gives essentially the same relation between theJ integral and the amount of crack growthc, as Rice, Drugan, and Sham's theoretical analysis for a crack growing in an elastic-perfectly plastic material under small scale yielding conditions. This paper extends the DBCS model analysis by incorporating work-hardening, and it is demonstrated that the relation betweenJ andc has the same form as for a nonwork-hardening material. Furthermore, it is predicted, for a high crack growth resistant material, that work-hardening decreases the steady-stateJ value, in accord with Dean and Hutchinson's numerical results, though it causes an increase in the initial slope of theJ —c curve, in accord with Sorensen's numerical results. These results are important as regards crack instability predictions under small scale yielding conditions.

---

Résumé Bien que de caractère hautement idéalisé, le modèle de zone plastique linéique DBCS fournit essentiellement la même relation entre l'intégraleJ et le gradient de croissance de la fissureC que l'analyse théorique de Rice, Drugan et Sham dans le cas d'une fissure croissant dans un matériau élastique/parfaitement plastique soumis à des conditions d'écoulement plastique à faible échelle. Le mémoire étend l'analyse du modèle DBCS en incorporant l'écrouissage; il démontre que la relation entreJ etC présente la même forme pour un matériau non sensible à l'écrouissage. De plus, on prédit que dans le cas d'un matériau à haute résistance à la croissance d'une fissure, l'écrouissage diminue la valeur deJ en état stable, conformément aux résultats numériques de Dean et Hutchinson, bien qu'il produise un accroissement de la pente initiale de la courbeJ/C, et ce en accord avec les résultats numériques de Sorensen. Ces résultats sont importants en ce qui regarde les prévisions d'instabilité d'une fissure sous des conditions d'écoulement plastique à faible échelle.

     

Dynamic shear band development in a thermally softening bimetallic body containing two voids

Summary We study the development of shear bands in a thermally softening viscoplastic prismatic body of square cross-section and containing two symmetrically placed thin layers of a different viscoplastic material and two elliptical voids with their major axes aligned along the vertical centroidal axis of the cross-section. One tip of each elliptical void is abutting the common interface between the layer and the matrix material. Two cases, i.e., when the yield stress of the material of the thin layer in a quasistatic simple compression test equals either five times or one-fifth that of the matrix material are studied. The body is deformed in plane strain compression at an average strain-rate of 5,000 sec^–1, and the deformations are assumed to be symmetrical about the centroidal axes.It is found that in each case shear bands initiate from points on the vertical traction free surfaces where the layer and the matrix materials meet. These bands propagate horizontally into the layer when it is made of a softer material and into the matrix along lines making an angle of ±45° with the vertical when the layer material is harder. In the former case, the band in the layer near the upper matrix/layer interface bifurcates into two bands, one propagating horizontally into the layer and then into other into the matrix material along the direction of the maximum shear stress. The band in the layer near the lower matrix/layer interface propagates horizontally first into the layer and then into the matrix material along the direction of the maximum shear stress. Irrespective of the value of the yield stress for the layer material, a band also initiates from the void tip abutting the layer/matrix interface. This band propagates initially along the layer/matrix interface and then into the matrix material along a line making an angle of approximately 45° with the vertical.     

X-ray diffraction studies on fatigue crack plastic zones developed under plane strain state conditions

An overview of the X-ray fractography technique, as performed on fatigue crack surfaces of several steels and Al-alloys under different loading conditions, is presented. The plastic zone sizes of fatigue cracks, for plane strain conditions, are measured from the in-depth distribution of residual stresses and X-ray diffraction peak broadening. In addition to the usual monotonic plastic zone size determination methodology, a model for the estimation of the reverse plastic zone size was established in the case of fatigue softening materials. Monotonic and cyclic plastic zone sizes are related to the stress intensity by, respectively, r_{pm = α (Kmax} /σ_ys )² and r_{pc = α} (ΔK/2σ′ys )2. The α-value, in the monotonic plastic zone size equation, increases as the yield strength of the material increases, following the relationship α = 0.196 [σ_ys /(129 + 0.928σ_ys )]2. The α-value versus σ_ys evolution has been understood through the influence of the hardening rate of materials on the plastic zone size. X-ray fractography has been applied to actual failure analyses to predict some aspects of the actual loadings.     

Effect of surface energy on the plastic behavior of crystalline thin films under plane strain constrained shear

In this work, a new continuum dislocation based model for crystal plasticity with surface energy effect is proposed. Based on the model, a thin film under plane constrained shear is considered. From the perspective of energy, the yield strength as a function of film thickness has been calculated which is achieved by comparing the energy due to elastic deformation, plastic deformation without surface energy and that with surface energy effect. According to the numerical results, the model including the impenetrable surface assumption can capture the surface dominated deformation mechanism for thin films of nanometer scale. In addition, the transition in dominant deformation mechanisms is also predicted for film thicknesses ranging from tens of nanometers to several microns.     

Life prediction based on weight‐averaged maximum shear strain range plane under multiaxial variable amplitude loading

Based on Wang and Brown's reversal counting method, a new approach to the determination of the critical plane is proposed by the defined plane with a weight‐averaged maximum shear strain range under multiaxial variable amplitude loading. According to the determined critical plane, a detailed procedure of multiaxial fatigue life prediction is introduced to predict lives in the low‐cycle multiaxial fatigue regime. The proposed approach is verified by two multiaxial fatigue damage models and Miner's linear cumulative damage law. The results showed that the proposed approach can effectively predict the orientation of the failure plane under multiaxial variable amplitude loading and give a satisfactory life prediction.     

Quasi-statically growing crack-tip fields in elastic perfectly plastic pressure-sensitive materials under plane strain conditions

Quasi-statically growing crack-tip fields in elastic perfectly plastic pressure-sensitive materials under plane strain conditions are investigated in this paper. The materials are assumed to follow the Drucker-Prager yield criterion and the normality flow rule. The asymptotic mode I crack-tip fields are assumed to follow the five-sector assembly of Drugan et al. (1982) for Mises materials. The crack-tip sectors, in turns, from the front of the crack tip are a constant stress sector, a centered fan sector, a non-singular plastic sector, an elastic sector and finally a trailing non-singular plastic sector bordering the crack face. The results of the asymptotic analysis show that as the pressure sensitivity increases, the plastic deformation shifts to the front of the tip, the angular span of the elastic unloading sector increases, and the angular span of the trailing non-singular plastic sector bordering the crack surface decreases. As the pressure sensitivity increases to about 0.6, the angular span of the trailing non-singular plastic sector almost vanishes. The effects of the border conditions between the centered fan sector and the first non-singular plastic sector on the solutions of the crack-tip fields for both Mises and pressure-sensitive materials are investigated in details. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of fabric anisotropy on shear localization in sand during plane strain compression

Summary The paper focuses on the effect of fabric anisotropy on shear localization in cohesionless granular materials. For the numerical simulation, a hypoplastic constitutive model was used. In order to take into account a characteristic length of the micro-structure, the constitutive model was extended to include the second gradient of the Euclidian norm of the deformation rate. The hypoplastic model captures the salient features of granular bodies in a wide range of density and pressure with a single set of parameters. Transversal isotropy is described by the dyadic product of the normal vector of the space orientation of the plane of symmetry. FE-simulations of plane strain compression under constant lateral pressure were carried out with a medium dense specimen for both uniform and stochastic distribution of the initial void ratio. The effect of the direction of the bedding plane and the initial void ratio distribution on the load-deformation behavior was investigated. Moreover, the location, thickness and inclination of the shear zone were also analyzed.     

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J₂ incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.     

Behaviour of voids in a shear field

When voids are present in a ductile material subject to a shear dominated stress state under low stress triaxiality the voids collapse to micro-cracks, which subsequently rotate and elongate in the shear field. In the present plane strain analyses for cylindrical voids a surface load normal to a plane connecting the ends of the micro-crack is used as an approximate representation of contact stresses during frictionless sliding. In a previous study of the same problem the author applied hydrostatic pressure inside the nearly closed micro-crack to approximate contact conditions. The transverse surface loads used in the present analyses avoid the tendency to unrealistically elongate the voids. It is found that even though the model applied here gives significantly later occurrence of a maximum overall shear stress than that found by using hydrostatic pressure, the present model does predict a maximum in all the cases analyzed and thus illustrates the micro-mechanism leading to failure of the material by localization of plastic flow.