Prediction of the Onset of Failure in Elastomeric Solids with Weld Lines being Represented as Localized Regions of Lower Density

2021 ◽  
pp. 1-41
Author(s):  
Chellappa Karunakaran ◽  
Alagappan Ponnalagu ◽  
Krishna Kannan ◽  
Kumbakonam Rajagopal
Keyword(s):  
Stress Concentrator ◽  
Weld Line ◽  
The Body ◽  
Reference Configuration ◽  
Line Defect ◽  
Stress Concentrators ◽  
Current Configuration

Abstract We study the initiation of damage in a polymeric body in which there is a line defect due to the formation of a “weld line” that occurs when two polymer streams join together and then solidify. We show that damage initiates in the region of weakness, namely the “weld line” based on a criterion for damage that was developed earlier in [1]. We also show that if there are other stress concentrators also additionally present, such as a hole, then there is a competition between the stresses induced due to the weakness and the stress as a consequence of the stress concentrator (in this instance a hole). This study adds more credence to the criterion for the initiation of damage that is based completely on knowledge of information at the current configuration of the body, that is, the criterion for damage is not based on the value of quantities that also need information based on a reference configuration such as the stress or strain.

scholarly journals On a possible methodology for identifying the initiation of damage of a class of polymeric materials

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160231 ◽  
Author(s):  
P. Alagappan ◽  
K. Kannan ◽  
K. R. Rajagopal
Keyword(s):  
Material Properties ◽  
Polymeric Materials ◽  
Damage Parameter ◽  
The Body ◽  
Experimental Results ◽  
Reference Configuration ◽  
Damage Criterion ◽  
Current Configuration ◽  
Polymeric Solid

In this paper, we provide a possible methodology for identifying the initiation of damage in a class of polymeric solids. Unlike most approaches to damage that introduce a damage parameter, which might be a scalar, vector or tensor, that depends on the stress or strain (that requires knowledge of an appropriate reference configuration in which the body was stress free and/or without any strain), we exploit knowledge of the fact that damage is invariably a consequence of the inhomogeneity of the body that makes the body locally ‘weak’ and the fact that the material properties of a body invariably depend on the density, among other variables that can be defined in the current configuration, of the body. This allows us to use density, for a class of polymeric materials, as a means to identify incipient damage in the body. The calculations that are carried out for the biaxial stretch of an inhomogeneous multi-network polymeric solid bears out the appropriateness of the thesis that the density of the body can be used to forecast the occurrence of damage, with the predictions of the theory agreeing well with experimental results. The study also suggests a meaningful damage criterion for the class of bodies being considered.

scholarly journals The Boundary Element Method and Path-independent Integrals in Sensitivity Analysis of Structures with Stress Concentration

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
T. Burczynski ◽  
M. Habarta
Keyword(s):  
Sensitivity Analysis ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Stress Concentrator ◽  
The Body ◽  
Numerical Verification ◽  
Shape Sensitivity ◽  
Stress Concentrations ◽  
Stress Concentrators ◽  
Element Method

This paper presents the implementation of the boundary element method to shape sensitivity analysis of elastic structures with stress concentrators. An elastic body which contains a number of voids (internal boundaries), playing the role of stress concentrators, is considered. We are interested in calculating the first order sensitivity of shape–dependent functionals with respect to the shape variation of the body domain. This task is accomplished using the adjoint variable method. As it has been shown by Dems and Mróz [10], for a basic transformation (i.e. a translation, a rotation or a scale change) of the body, the sensitivity of the considered functional takes the form of a path-independent integral (PII) whose integrand depends on the primary and adjoint state fields, along an arbitrary path (curve in 2D, surface in 3D), enclosing the transformed stress concentrator (void). It is very important for numerical computations, because we can compute this integral along the path placed far from the stress concentrator to eliminate the negative influence of stress concentrations on the accuracy of calculations. The boundary element method (BEM) is used to solve both primary and adjoint problems. Some important cases of adjoint problems related to functionals are analyzed in the paper. A thorough numerical verification of the proposed method is performed in this work. The presented method of sensitivity analysis is utilised in gradient-based optimization and identification problems. Numerical examples of optimization and identification are shown in this paper.

The use of computational contact mechanics approaches to assess the performance of parts bearing stress concentrators

2020 ◽  
Vol 1 (103) ◽  
pp. 25-32
Author(s):  
B.A. Lyashenko ◽  
Z.A. Stotsko ◽  
O.A. Kuzin ◽  
M.O. Kuzin
Keyword(s):  
Surface Stress ◽  
Stress Concentrator ◽  
Contact Strength ◽  
Stress Concentrators ◽  
Computational Contact Mechanics ◽  
Local Properties ◽  
Non Local ◽  
Bearing Stress ◽  
The Cost ◽  
Inhomogeneous Properties

Purpose: The purpose of this work is to build new computational schemes for assessing the strength parameters of parts with inhomogeneous properties of surface layers in the presence of stress concentrators. Design/methodology/approach: Using the developed approaches of mathematical modeling and open software for calculating the structures of the FEM - FEniCS, the required thickness of the hardened zones of parts has been established, which ensures their minimum softening during operation, depending on the characteristics of the stress concentrator. Findings: It is shown that for each size of the surface stress concentrator there is a critical value of the hardening thickness, the excess of which does not affect the operational strength of the parts, but increases the cost of technological operations. Research limitations/implications: In this article proposes a method for calculating the influence of the dimensional characteristics of hardening zones on the contact strength of parts with stress concentrators under conditions of prevailing power loads. Practical implications: The results obtained in this work were used to determine the technological modes of plasma hardening, which ensure an increase in the contact strength of parts with stress concentrators, depending on their dimensional characteristics. Originality/value: Using the approaches of computational mechanics and mathematical and computer modeling, methods for controlling the contact strength of parts with inhomogeneous non-local properties in the presence of a surface stress concentrator are proposed for the first time.

Comparison of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation by Means of a Simplified Strain Formulation

2003 ◽  
Author(s):  
J. Gerstmayr
Keyword(s):  
Stiffness Matrix ◽  
Small Strain ◽  
Frame Of Reference ◽  
The Body ◽  
Reference Configuration ◽  
Absolute Nodal Coordinate ◽  
Floating Frame Of Reference ◽  
Fixed Reference ◽  
Floating Frame ◽  
Strain Model

The floating frame of reference (FFR) formulation and the absolute nodal coordinate (ANC) formulation are often used for the modeling of multibody systems. In the present work a simplified strain model is derived for the ANC formulation which is equivalent to the (small strain) FFR formulation. The simplified strain model is based on a co-rotated reference configuration and the deformation is assumed to be small with respect to this configuration. This configuration is described by a translation vector and a rotation matrix which are both determined from the motion of the body with respect to its fixed reference. The ANC formulation with simplified strain leads to a constant mass matrix. The stiffness matrix consists of two parts: One part depends on the small-strain stiffness matrix of the body in the fixed reference configuration which is rotated by the rotation matrix and a second nonlinear part which depends quadratically on small strains. Both formulations represent displacements and deformations differently but lead to exactly the same results in the case of equivalent floating reference configurations. The relationship of both formulations is compared in a 2D example problem of a rotating hinged plate. A detailed description of the modelling in both cases as well as numerical results are presented.

Stress Effects on Activity of Primary Cracks Initiating at Stress Concentrator

2003 ◽  
Vol 17 (08n09) ◽  
pp. 1567-1572
Author(s):  
Sam Hong Song ◽  
Jin Bong Kim
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Stress Distribution ◽  
Stress Concentrator ◽  
Mechanical Analysis ◽  
Mean Stress ◽  
Stress Concentrators ◽  
Stress Effects ◽  
The Mean ◽  
As Stress

This study has been performed to investigate the stress distribution around defects that behave as stress concentrators and fracture mechanical analysis for cracks initiating at stress concentrators. The stress distribution was analyzed using Finite Element Method and non-dimensional stress intensity factor was determined by the mean stress method. This method could be applied to determine the activity of primary crack initiated at the stress concentrator in experiment. In addition, stress interaction effects around defects and cracks were compared.

scholarly journals Modeling the deformation process of a plate with a stress concentrator taking into account the postcritical stage of material deformation

2020 ◽  
pp. 32-40
Author(s):  
V. E Wildemann ◽  
M. P Tretyakov ◽  
A. I Mugaratov
Keyword(s):  
External Load ◽  
Structural Damage ◽  
Stress Concentrator ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Stress Concentrators ◽  
Postcritical Deformation ◽  
Material Deformation ◽  
Strength And Deformation ◽  
Deformation Mechanics

Postcritical deformation of a material is a process which is characterized by a decrease of stress during growing deformations as a result of accumulation of structural damage. The design becomes unable to withstand the external load only when zones with weakened connections are developed enough. Evolution of postcritical deformation zones can occur with an increase of the external load applied to the construction. It means that taking into account the softening of the material allows determining the strength and deformation reserves of constructions more accurately. The mathematical formulation of the boundary value problem of supercritical deformation mechanics is given in the paper. The features of the experimental study of the postcritical stage of material deformation are listed. Strain curves of various steels with a long section of softening are obtained. Numerical solutions for the problems of deforming a thin plate with stress concentrators of different geometries under kinematic loading are obtained. Piecewise linear approximations and real strain curves of steel 20 and steel 40Cr4 obtained experimentally are considered. The evolution of zones of postcritical deformation in the material is considered. The correspondence between the value of the decline modulus and the nature of the evolution of the softening zones is determined. A stress plot is constructed that reflects how the complete material deformation diagram is realized near the concentrator. The calculated loading diagrams are constructed. It is noted that even after the appearance of softening zones, an increase in external load is possible. The strength and deformation resources of structures are determined, and the influence of the geometry of the stress concentrator on their values is considered. It is noted that the consideration of softening in modeling the behavior of structures with stress concentrators is appropriate.

Multigenerational Interstitial Growth of Biological Tissues

2010 ◽  
Author(s):  
Gerard A. Ateshian ◽  
Tim Ricken
Keyword(s):  
Constitutive Relations ◽  
Biological Tissues ◽  
Reference Configuration ◽  
Solid Matrix ◽  
Current Configuration ◽  
Interstitial Growth

The objective of this study is to formulate a theory for multigenerational interstitial growth of biological tissues whereby each generation has a distinct reference configuration determined at the time of its deposition. In this model, the solid matrix of a growing tissue consists of a multiplicity of intermingled bodies, each of which represents a generation, all of which are constrained to move together in the current configuration. This proposed framework builds on the concept of constrained mixtures of solids originally formulated by Humphrey and Rajagopal (2002). The specific aim is to determine the form of constitutive relations for the solid constituents of a multigenerational tissue, and provide simple illustrations of the theory.

Study on the Roller-Bending Simulation to Promote Productivity in the HINGE STRAP Forming System

2011 ◽  
Vol 695 ◽  
pp. 149-152 ◽  
Author(s):  
Sung Ho Chang ◽  
Young Moo Heo
Keyword(s):  
Mechanical Properties ◽  
Process Simulation ◽  
Weld Line ◽  
Accurate Estimate ◽  
The Body ◽  
Bending Process ◽  
Pressure Cylinder ◽  
Increase Productivity ◽  
Original Metal

The purpose of present study was to increase productivity and to promote the quality of the part in the forming system for hinge strap in automobile. So the roller-bending simulation was carried out to develop the forming system for the hinge strap. A square tube used in the roller-bending for the hinge strap was fabricated using process of the sheet forming and the welding. So study on the mechanical properties of the original metal sheet (SPCC 1.6t) and weld-line (including a HAZ) were performed before the roller-bending simulation. And the body forces of the roller (rigid body) in the roller-bending process simulation were calculated to make an accurate estimate the capacity of the oil pressure cylinder for a pressure device. Then the roller-bending process was divided into 5 steps for the simulation for validating the effect of the bending velocity on the springback. At the end, the shape after springback was estimated. The result was adopted in the design for the bending die.

scholarly journals Use of different methods of local SPD (surface plastic deformation) to reduce stress concentrator impact upon profile surfaces of transport machinery parts

2019 ◽  
Vol 2019 (7) ◽  
pp. 42-48
Author(s):  
Владимир Макаров ◽  
Vladimir Makarov ◽  
Александр Горбунов ◽  
Alexander Gorbunov
Keyword(s):  
Plastic Deformation ◽  
Stress Concentrator ◽  
Fatigue Cracks ◽  
Surface Plastic Deformation ◽  
Surface Plastic ◽  
Local Surface ◽  
Complex Profile ◽  
Stress Concentrators ◽  
Transition Areas ◽  
Technological Stress

It is defined that in the course of machining complex profile parts operating under heavy alternating loads, in critical transition areas of profile conjugated surfaces there are formed local technological stress concentrators promoting the formation and growth of fatigue cracks and further destruction of operating parts. There are developed and introduced methods to reduce the values of such stress concentrators on the basis of the application of different methods of local surface plastic deformation.

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