scholarly journals Non-Linear Analysis of Mode II Fracture in the end Notched Flexure Beam

2016 ◽  
Vol 46 (1) ◽  
pp. 53-64
Author(s):  
V. Rizov
Keyword(s):  
Strain Curve ◽  
Beam Theory ◽  
Integral Approach ◽  
J Integral ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Non Linear ◽  
Tension And Compression ◽  
Parametric Analyses ◽  
Strain Equation

Abstract Analysis is carried-out of fracture in the End Notched Flex- ure (ENF) beam configuration, taking into account the material nonlin- earity. For this purpose, the J-integral approach is applied. A non-linear model, based on the Classical beam theory is used. The mechanical be- haviour of the ENF configuration is described by the Ramberg-Osgood stress-strain curve. It is assumed that the material possesses the same properties in tension and compression. The influence is evaluated of the material constants in the Ramberg-Osgood stress-strain equation on the fracture behaviour. The effect of the crack length on the J-integral value is investigated, too. The analytical approach, developed in the present paper, is very useful for parametric analyses, since the simple formulae obtained capture the essentials of the non-linear fracture in the ENF con- figuration.

Delamination analysis of a layered elastic-plastic beam

2017 ◽  
Vol 8 (5) ◽  
pp. 516-529 ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Fracture Behaviour ◽  
Strain Curve ◽  
Integral Approach ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Lap Shear ◽  
Delamination Fracture ◽  
Non Linear

Purpose The purpose of this paper is to perform a theoretical analysis of delamination fracture behaviour of the Crack Lap Shear layered beam configuration taking into account the material non-linearity. A delamination crack located arbitrarily along the beam height was considered in this study. Design/methodology/approach The beam mechanical behaviour was described by using the Ramberg-Osgood stress-strain relation. Fracture was analysed by applying the J-integral approach. Besides by using symmetric Ramberg-Osgood stress-strain curve, fracture was investigated also by Ramberg-Osgood stress-strain curve that is not symmetric with respect to tension and compression. The J-integral solutions were verified by performing elastic-plastic analyses of the strain energy release rate. Findings The effects of crack location and material properties on the non-linear fracture behaviour were evaluated. It was found that the material non-linearity leads to increase of the J-integral values. Therefore, the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members composed by layered materials. The analytical solutions derived are very useful for parametric investigations of delamination fracture with considering the material non-linearity. The results obtained can be applied for optimisation of the beam structure with respect to fracture performance. Originality/value The present study contributes for the understanding of delamination fracture in layered beams that exhibit non-linear material behaviour.

Uniaxial Deformation of Rubber Cylinders

1995 ◽  
Vol 68 (5) ◽  
pp. 739-745 ◽  
Author(s):  
P. H. Mott ◽  
C. M. Roland
Keyword(s):  
Strain Curve ◽  
Uniaxial Deformation ◽  
Deflection Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Optical Birefringence ◽  
Parabolic Profile ◽  
Strain Data ◽  
Tension And Compression ◽  
Actual Stress

Abstract Stress, strain and optical birefringence measurements were made on elastomeric cylinders deformed in tension and compression. The birefringence data enables the actual stress to be determined even when the deformation is not homogeneous. In the absence of lubricant, uniaxially loaded rubber cylinders deviate from homogeneous deformation due to bonding of the cylinder ends. The existing analysis to correct the force-deflection curve for the effect of this sticking, strictly valid for infinitesimal strains, is premised on the idea that the deformed cylinder has a parabolic profile. Experimentally, however, it was found that slender rubber cylinders assume a much flatter profile, while maintaining constant volume, when deformed. Nevertheless, the accuracy of the stress-strain curve when the standard correction is applied turns out to be quite good, partially a result of cancellation of two, relatively small, errors. This accuracy was assessed by comparison of force-deflection data from bonded cylinders both to stress-strain data obtained on lubricated cylinders and to the stresses deduced from the measured birefringence.

Experimental Setup for the Determination of Mechanical Solder Materials Properties at Elevated Temperatures

2010 ◽  
Vol 638-642 ◽  
pp. 3793-3798
Author(s):  
Wolfgang H. Müller ◽  
Holger Worrack ◽  
Jens Sterthaus
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Elevated Temperatures ◽  
Young's Modulus ◽  
Linear Optimization ◽  
Strain Curve ◽  
Stress And Strain ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Non Linear

The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young’s modulus, yield stress, and hardness are of great interest. Moreover, a complete stress-strain curve is desirable for a detailed material characterization and simulation of a component, e.g., by Finite Elements (FE). However, since the amount of matter is so small and it is the intention to describe its behavior as realistic as possible, miniature tests are used for measuring the mechanical properties. In this paper two miniature tests are presented for this purpose, a mini-uniaxial-tension-test and a nanoindenter experiment. In the tensile test the axial load is prescribed and the corresponding extension of the specimen length is recorded, both of which determines the stress-strain- curve directly. The stress-strain curves are analyzed by assuming a non-linear relationship between stress and strain of the Ramberg-Osgood type and by fitting the corresponding parameters to the experimental data (obtained for various microelectronic solders) by means of a non-linear optimization routine. For a detailed analysis of very local mechanical properties nanoindentation is used, resulting primarily in load vs. indentation-depth data. According to the procedure of Oliver and Pharr this data can be used to obtain hardness and Young’s modulus but not a complete stress-strain curve, at least not directly. In order to obtain such a stress-strain-curve, the nanoindentation experiment is combined with FE and the coefficients involved in the corresponding constitutive equations for stress and strain are obtained by means of the inverse method. The stress-strain curves from nanoindentation and tensile tests are compared for two mate-rials (aluminum and steel). Differences are explained in terms of the locality of the measurement. Finally, material properties at elevated temperature are of particular interest in order to characterize the materials even more completely. We describe the setup for hot stage nanoindentation tests in context with first results for selected materials.

Non-linear delamination fracture analysis by using power-law hardening

2016 ◽  
Vol 12 (1) ◽  
pp. 80-92 ◽  
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Power Law ◽  
Strain Curve ◽  
Fracture Analysis ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Content Type ◽  
Elastic Plastic ◽  
Linear Fracture ◽  
Delamination Fracture ◽  
Non Linear

Purpose – The purpose of this paper is to perform a theoretical analysis of non-linear delamination fracture in cantilever beam opened notch (CBON) configuration. It is assumed that the non-linear mechanical behavior of the CBON can be described by using a stress-strain curve with power-law hardening. Design/methodology/approach – The fracture analysis is carried-out by applying the integration contour independent J-integral. For this purpose, a model based on the technical beam theory is used. Equation is derived for determination of the CBON specimen curvature in elastic-plastic stage of deformation. The equation is solved by using the MatLab program system. Solutions of the J-integral are obtained at linear-elastic as well as elastic-plastic behavior of the CBON. The influence of the power-law exponent on the non-linear fracture is evaluated. Findings – The analysis reveals that the J-integral value increases when the exponent of the power-law increases. The solution obtained here is very useful for parametric analyses of the non-linear fracture behavior, since the simple formulas derived capture the essentials of the fracture response. Practical implications – Beside for parametric investigations, the solution obtained here can also be applied for calculating the critical J-integral value at non-linear behavior using experimentally determined critical fracture load at the onset of crack growth from the initial crack tip position in the CBON configuration. Originality/value – An analysis is performed of the non-linear fracture in the CBON configuration by applying the J-integral approach, assuming that the mechanical response can be modeled using a stress-strain curve with power-law hardening.

Experimental Research on Constitute Relation of Concrete under Uniaxial Tension and Compression with Different Strain Rate

2011 ◽  
Vol 250-253 ◽  
pp. 3279-3283 ◽  
Author(s):  
Hai Bin Chen ◽  
You Po Su ◽  
Jun Wei Xing ◽  
Yu Min Zhang
Keyword(s):  
Structural Analysis ◽  
Strain Rate ◽  
Uniaxial Tension ◽  
Theoretical Basis ◽  
Strain Curve ◽  
Strain Ratio ◽  
Test Device ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Tension And Compression

The constitutive relation of concrete under uniaxial tension and compression is an essential theoretical basis for structural analysis of concrete. Because of the lack of sufficient stiffness for ordinary test device, a stable decline branch of stress-strain curve could not be obtained. The condition of realizing the stress-strain complete curve for concrete uniaxial tension and compression is derived. The experiment device for uniaxial tension and compression was designed and fabricated with increasing stiffness method. Experiments were carried out for concrete with grade C30~C60 and strain rate 10-5/s~10-2/s. The equation for stress-strain curve in the rising branch were obtained and so were the complete stress-strain curve of uniaxial tension and compression under different strain ratio, which provide the theoretical basis for concrete structural analysis.

scholarly journals A 3-D finite element modeling for the textile-reinforced concrete plates under tensile load using a non-linear behaviour for cementitious matrix

2021 ◽  
Vol 15 (1) ◽  
pp. 67-78
Author(s):  
Tran Manh Tien ◽  
Xuan Hong Vu ◽  
Dao Phuc Lam ◽  
Pham Duc Tho
Keyword(s):  
Reinforced Concrete ◽  
Mechanical Behavior ◽  
Tensile Load ◽  
Strain Curve ◽  
Numerical Results ◽  
Textile Reinforced Concrete ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Cementitious Matrix ◽  
Non Linear

A big question in the numerical approaches for the mechanical behavior of the textile-reinforced concrete (TRC) composite under tensile loading is how to model the cracking of the cementitious matrix. This paper presents numerical results of 3-D modeling of TRC composite in which the non-linear behavior model was used by considering the cracking for the cementitious matrix. The input data based on the experimental results in the literature. As numerical results, the TRC composite provides a strain-hardening behavior with three phases in which the second one is characterized by the drops in stress on the stress-strain curve. Furthermore, this model could show the failure mode of the TRC specimen with the multi-cracking on its surface after the numerical tests. From this model, the development of a crack from micro-crack to macro at a cross-section was highlighted. The stress jumps in reinforcement textile after each crack was also observed and analyzed. In comparison with the experiment, a good agreement between both results was found for all cases of this study. A parametric study could show the effect of the length and position of the measurement zone on the stress-strain curve of TRC’s mechanical behavior. Keywords: textile reinforced concrete (TRC); cementitious matrix; textile reinforcement; mechanical behaviour; numerical modeling.

scholarly journals Non-linear finite element analysis of a Ti6Al4V/Inconel 625 joint obtained by explosion welding for sub-sea applications

2021 ◽  
Vol 38 (1) ◽  
pp. 13-16
Author(s):  
Pasqualino Corigliano
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Strain Curve ◽  
Explosion Welding ◽  
Inconel 625 ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Element Analysis ◽  
Linear Finite Element ◽  
Non Linear

Industries have shown interest in the use of dissimilar metals to make corrosion-resistant materials combined with good mechanical properties in marine environments. Explosive welding can be considered a good method for joining dissimilar materials to prevent galvanic corrosion. The aim of the present study was to simulate the non-linear behaviour of a Ti6Al4V/Inconel 625 welded joint obtained by explosion welding from the values of the tensile ultimate strength and yielding strength of the parent materials. The present study compared the stress-strain curve from tensile loading obtained by the non-linear finite element analysis with the experimental stress-strain curve of a bimetallic joint. The applied method provides useful information for the development of models and the prediction of the structural behaviour of Ti6Al4V/Inconel 625 explosive welded joints.

Deformation Behavior of a Magnesium Alloy Sheet with Random Crystallographic Orientations

2014 ◽  
Vol 611-612 ◽  
pp. 27-32 ◽  
Author(s):  
Takayuki Hama ◽  
Tsuyoshi Mayama ◽  
Hirohiko Takuda
Keyword(s):  
Deformation Behavior ◽  
Strain Path ◽  
Strain Curve ◽  
Path Dependency ◽  
Alloy Sheet ◽  
Mg Alloy ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Tension And Compression ◽  
Crystallographic Orientations

In the present study, the deformation behavior of a cast Mg alloy sheet that had random crystallographic orientations was studied both experimentally and numerically. Although the crystallographic orientations were random, the stress-strain curve was asymmetric between tension and compression: the flow stress under tension was higher than that of compression. Moreover, the stress-strain curve exhibited a strain path dependency: a slightly sigmoidal curve occurred under tension following compression, while it did not occur under compression following tension. Clearly, such tendencies were similar to those observed in rolled Mg alloy sheets although the tendencies were less pronounced in the cast Mg alloy sheet. A crystal plasticity finite-element method was used to understand the mechanism of these results. Simulation results showed that the asymmetry and the strain path dependency in the stress-strain curves occurred in the cast Mg alloy sheet because of the asymmetry in the activity of twinning between tension and compression as in the case of rolled Mg alloy sheets.

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