The Bending Strength of Materials with a Non‐Linear Stress‐Strain Curve

1947 ◽  
Vol 19 (7) ◽  
pp. 212-216 ◽  
Author(s):  
S.S. Gill
Keyword(s):  
Bending Strength ◽  
Strain Curve ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Strength Of Materials ◽  
Non Linear

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.

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.

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.

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.

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