Nature of the friction deformation of the surface layers of polymethyl methacrylate

The surface deformation of amorphous thermoplastics (polymethyl methacrylate) by a spherical steel indentor has been investigated at various sliding velocities. Small velocities correspond to elastic and forced-elastic deformation of the surface layers and asperities. At temperatures corresponding to the high-elastic state the deformed surface layer completely recovers its shape. As the sliding velocity increases, the forced-elastic deformation is localized in a thinner layer of plastic. Starting from a certain velocity, depending on the temperature and the activation energy for transition of the chain segments from one equilibrium position to another in the process of thermal motion, the deformation of the surface layers and asperities becomes purely elastic. In the event of elastic deformation at pressures above a certain value the surface layer of plastic suffers brittle fracture in the tensile zone behind the indentor.Mekhanika Polimerov, Vol. 4, No. 1, pp. 90–94, 1968.     

Concentrators of deformations and fracture of plastic bodies

An approach to the investigation of shape discontinuity regions as strain concentrators is proposed. The near-concentrator strain fields are determined on the basis of the theory of ideal rigid-plastic body; under the condition of plane deformation, their determination is reduced to integration of ordinary differential equations. The deformation as a function of the location of the plastic region and its shape evolution in the process of plastic flow is studied. The plastic flow is demonstrated to be not unique (within the framework of solution completeness). A deformation criterion for the choice of the preferred plastic flow is suggested. The fracture of a V-notched strip is considered. On the basis of the solutions obtained, an approach to the investigation of the fracture processes for more complicated models is formulated.     

Probabilistic modeling and simulation of multiple surface crack propagation and coalescence

In the low cycle fatigue (LCF) regime, fatigue failure of metallic materials with high strength and less impurities generally dominates by multiple surface crack propagation and coalescence, in which its final failure shows a stochastic nature on crack initiation, propagation and coalescence under cyclic loadings. According to this, the competing failure modes of multiple surface cracks and interior cracks are studied through coupling numerical simulations with fracture mechanics methods. In particular, a probabilistic procedure for modeling multiple surface crack propagation and coalescence is established by incorporating Monte Carlo simulation with experimental evidences, including surface crack density and crack length distributions measured from LCF replica tests of 30NiCrMoV12 steel. In addition, it calculates the probability of coalescence of neighboring cracks with allowance for their interactions and local plastic deformation at the crack tips. Finally, it estimates the remaining usage lives of specimens from initial state to critical cracks by propagation and coalescence of dispersed cracks.     

Three-Dimensional Computational Analysis of Stress State Transition in Through-Cracked Plates

Stress state is a main parameter within fracture mechanics. It has a major influence on different phenomena, namely those involving diffusion, plastic deformation, and brittle fracture. As is well-known, in the near-surface regions of a crack front, the plane stress state dominates, while at interior positions the plane strain state prevails. The main objective here is to examine the extent of surface regions in through-cracked planar geometries subjected to cyclic loading. Two constitutive material models were developed to characterise the stress state along the crack front. A new criterion based on the h stress triaxiality parameter was proposed to define the transition between surface and near-surface regions. Finally, a linear relation between the stable value of the extent of surface region and the maximum stress intensity factor was established.     

Plastic zone development in dynamic tear-type test specimens

The J-integral is a fracture criterion, which permits measurement of the fracture toughness of a specimen where fracture occurs in the elastic–plastic regime. An understanding of the ratio of plastic zone size (radius) to the crack tip blunting (stretch zone) is required to determine the upper temperature for transition curves, where elastic–plastic fracture becomes invalid and general yielding occurs. This study endeavors to acquire this ratio using finite element techniques. The development of the plastic zone in dynamic tear (DT) specimens and non-standard three-point bending fracture test specimens was the main focus of the study. The ABAQUS finite element software was used to model the elastic–plastic behaviour of the specimens. The cracks in the specimens were induced by pressing the notch followed by fatigue cracking at 30–40% of the limit loads. The shapes of these cracks were adequately modelled in the finite element analysis. The specimens were made of 350WT steel and 304 stainless steel materials and were loaded until fixed amounts of permanent deformation were recorded. Results were obtained in the form of plots, showing the progression of the plastic zone around the crack tip. For each case, mid-point plastic deflection, stretch zone width and plastic zone radius were computed.     

Prediction of changes in the strength of filled thermoplastics upon aging in an oxidizing atmosphere

Problems related to analyzing specimens with damaged surface layers have been examined using polyamide, trioxane—dioxolane copolymer, and polycarbonate as source materials. A model was developed for the brittle fracture of block specimens with damaged surface layers, which provides an estimate of the restraints to plastic deformation in these layers. Three segments are seen in the strength—time curves featuring 1) increasing strength, 2) decreased strength with brittle fracture, and 3) constant low strength. The strength of filled specimens of a specific period permits us to evaluate the effect of the filler on the fracture resistance of the matrix. A method was proposed for predicting the strength of filled samples using the matrix aging data.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 3, pp. 375–380, May–June, 1993.     

Damage and fracture behavior in dynamic tension tests: Modelling and numerical simulations

The continuum damage model is based on a general thermodynamic framework for the modeling of rate and temperature dependent behavior of anisotropically damaged elastic-plastic materials subjected to fast deformation. The introduction of damaged and fictitious undamaged configurations allows the definition of damage tensors and the corresponding free energy functions lead to material laws affected by damage and temperature. The damage condition and the corresponding damage rule strongly depend on stress triaxiality. Furthermore, the rate and temperature dependence is reflected in a multiplicative decomposition of the plastic hardening and damage softening functions. The macro crack behavior is characterized by a triaxiality dependent fracture criterion. The continuum damage model is implemented into LS-DYNA as user defined material model. Corresponding numerical simulations of unnotched and notched tension tests with high strain rates demonstrate the plastic and damage processes during the deformation leading to final fracture numerically predicted by an element erosion technique. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Role of the supermolecular structure of PMM in the morphology of fracture and features introduced by the type of loading

The spherulitic supermolecular structure of PMM, expressed in the fracture surface, determines the fracture pattern and kinetics. The effect of the type of loading on the morphology of the fracture surface is described. Banding of the fracture surface is attributed to periodic energy pulses leading to quasi-brittle fracture at the moving crack front and selective local crack development at the band edges.Riga Lenin Komsomol Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 776–782, September–October, 1968.     

On Plane Dilatational Plasticity

The plane plastic deformation of a generally anisotropic rigid-plastic material which possesses a yield condition dependent upon mean triaxial stress and which, through the classical associated flow rule, exhibits plastic dilatation, is considered. This model is used to represent the behavior of micro-porous ductile metals in which the micro-cavities may be strongly aligned due to large prior plastic strains, as for example the material surrounding the tip of an extending notch in a ductile metal. It is shown that the stress and velocity fields are hyperbolic where a line of vanishing extension rate may be found in the plane of deformation, and that the characteristics of both the stress and velocity fields coincide with the lines of vanishing extension rate. Coincidence of the characteristics of stress and velocity fields in general anisotropic plastic bodies seems not to have been expected in earlier writings, but is a natural consequence of the associated flow rule. Simple means of determining whether a given stress state at yield lies in a hyperbolic or elliptic field are discussed. The role of characteristics in providing ductile fracture nuclei is discussed.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.     

基于断裂能的岩土节理弹性-软化塑性本构模型

基于准脆性材料的断裂力学和塑性理论,提出了用于岩土节理软化行为描述的弹性软化塑性本构模型.模型的主要特点是:1)节理材料的软化塑性和扩容特性直接与断裂失效过程相联系,所采用的材料参数比已有的弹塑性软化模型所用的参数少;2)模型可以描述混合断裂失效及相应的摩擦滑动,具有较广的适用性.     

Configurational Forces in Crystal Plasticity

The surface morphology of micro machined surfaces depends on the heterogeneous microstructure. A crystal plasticity model is used to describe the plastic deformation in cp-titanium with its hcp crystal structure. Therefore the basal and prismatic slip systems are taken into account. Furthermore, self and latent hardening are considered. The rate dependency is motivated by a visco plastic evolution law. The cutting process of cp-titanium is modeled within the concept of configurational forces for a standard dissipative media. This framework is implemented into the finite element method. An example illustrates the effects of the microstructure on plastic deformation and configurational forces. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of shear stiffness and concrete wedge cone failure on fracture of a fiber-reinforced plastic rod at an intersection with a concrete crack

Experimental results of model speciments in which FRP rods fractured due to local deformation at a crack intersection in a concrete member were analyzed by a 3D nonlinear finite element method in which orthogonal anisotropy of the FRP rod was considered. The analytical results indicated that accurate prediction of shear modulus of the FRP rod and size of concrete wedge cone failure around the FRP rod was significant to predict deformation and fracture of the FRP rod. FRP rods as reinforcement in concrete members, the small shear modulus, because of the orthogonal anisotropy and the wedge cone failure, may prevent the FRP rod from fracturing at a very low tensile stress due to the local deformation at the crack intersection.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Published in Mekhanika Kompozitnykh Materialov, Vol. 21, No. 2, pp. 158–166, March–April, 1996.     

Variational approach to formation of misoriented microstructures in plastic deformation

The formation of misoriented microstructures in plastic deformation is explained within the framework of continuum mechanics as a result of the reduction of the energetically costly hardening in multislip by local lattice rotations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local Gromov–Witten invariants of cubic surfaces via nef toric degeneration

We compute local Gromov–Witten invariants of cubic surfaces at all genera. We use a deformation a of cubic surface to a nef toric surface and the deformation invariance of Gromov–Witten invariants.     

Relation between local strains theory and deformation theory in the problem of stability of inelastic shells

In accordance with the theory of local plastic strains and the deformation theory of plasticity the coefficients of the compliance matrices are determined for the problem of stability of inelastic shells in the uniaxial precritical stress state. A comparison of the compliance matrices shows that for integration over a complete sphere the results obtained using the local strains theory and deformation theory are very close.Mekhanika Polimerov, Vol. 1, No. 6, pp. 54–60, 1965     

Geometrical super-elements for elasto-plastic shells with large deformation

This paper presents the application of the so-called Geometrical Elements Method (Lukasiewicz and Szyszkowski, 1974; Pogorelov, 1967) to the solution of elasto-plastic problems of shells. The approach is based on the observation that, during large deformations, the shell structure deforms in a nearly isometrical manner. Therefore, its deformed shape can be determined and analysed making use of the Gauss theorem according to which the Gaussian curvature of the isometrically deformed surface remains unchanged. The shell structure is subdivided into elements of two kinds: purely-isometrically deformed elements and quasi-isometrically deformed elements. The equilibrium of the whole structure is defined by the stationary value of the Hamiltonian function which requires the calculation of the strain energy in the elements. This can easily be obtained if we recognize that the isometrically deformed elements contain only bending energy. Using the method described, we are able to significantly the number of unknown values defining the shape of the deformed structure. The problem is reduced to the numerical evaluation of the minimum of a function of many variables. The elasto-plastic state of stress of the plastic material in the structure canbe determined by using the deformation theory of plasticity or the theory of plastic flow. Also, the strains and stresses in the plastic regions are the only functions of the assumed displacements field. The corresponding energy of the plastic deformation can easily be evaluated and added to the minimized functionals. For example, the elasto-plastic behaviour of a spherical shell under a concentrated load is studied. The solution obtained defines the large deformation behaviour and the motion of the plastic zones on the surface of the shell.     

An enhanced model for probabilistic cleavage fracture assessment considering local constraint effects

The present study is concerned with the development of an enhanced probabilistic model for cleavage assessment of ferritic steels. An enhanced model for the probabilistic cleavage fracture assessment has to consider the conditions for both, nucleation and propagation of micro defects. Hence, a propagation based model is enhanced by a combination of the local plastic strain and the local stress triaxiality to account for the nucleation of potentially critical micro defects. The formulation of the new model is based on the local mechanical field quantities determined numerically at the cleavage origins for a variety of standard deep and shallow crack specimens as well as for small scale cruciform bending specimens. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation

In the sheet bulk metal forming field, the strict geometrical requirements of the workpieces result in a need of a precise prediction of the material behaviour. The simulation of such forming processes requires a valid material model, performing well for a huge variety of different geometrical characteristics and finite deformation. Because of the crystalline nature of metals, anisotropies have to be taken into account. Macroscopically observable plastic deformation is traced back to dislocations within considered slip systems in the crystals causing plastic anisotropy on the microscopic and the macroscopic level. A finite crystal plasticity model is used to model polycrystalline materials in representative volume elements (RVEs) of the microstructure. A multiplicative decomposition of the deformation gradient into elastic and plastic parts is performed, as well as a volumetric-deviatoric split of the elastic contribution. In order to circumvent singularities stemming from the linear dependency of the slip system vectors, a viscoplastic power-law is introduced providing the evolution of the plastic slips and slip resistances. The model is validated with experimental microstructural data under deformation. The validation on the macroscopic scale is performed through the reproduction of the experimentally calculated initial yield surface. Additionally, homogenised stress-strain curves from the microstructure build the outcome for a suitable effective material model. Through optimisation techniques, effective material parameters can be determined and compared to results from real forming processes. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)