scholarly journals Strain Energy Density as Failure Criterion for Quasi-Static Uni-axial Tensile Loading

2021 ◽  
Vol 15 (57) ◽  
pp. 331-349
Author(s):  
Andrea Kusch ◽  
Simone Salamina ◽  
Daniele Crivelli ◽  
Filippo Berto
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Tensile Load ◽  
Strain Curve ◽  
Material Behavior ◽  
Uniaxial Tensile ◽  
Notched Specimens ◽  
Nonlinear Stress

Strain energy density is successfully used as criterion for failure assessment of brittle and quasi-brittle material behavior. This work investigates the possibility to use this method to predict the strength of V-notched specimens made of PMMA under static uniaxial tensile load. Samples are characterized by a variability of notch root radii and notch opening angles. Notched specimens fail with a quasi-brittle behavior, albeit PMMA has a nonlinear stress strain curve at room temperature. The notch root radius has most influence on the strength of the specimen, whereas the angle is less relevant. The value of the strain energy density is computed by means of finite element analysis, the material is considered as linear elastic. Failure prediction, based on the critical value of the strain energy density in a well-defined volume surrounding the notch tip, show very good agreement (error <15%) with experimental data.

Application of the Strain Energy Density Criterion to the Estimation of Fracture Loads in Structural Steel S355J2 at Lower Shelf Temperatures

2017 ◽  
Author(s):  
Sergio Cicero ◽  
Francisco Ibáñez ◽  
Isabela Procopio ◽  
Virginia Madrazo
Keyword(s):  
Energy Density ◽  
Structural Steel ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Input Parameter ◽  
Fracture Load ◽  
Notched Specimens ◽  
Fracture Tests ◽  
Material Fracture ◽  
Cracked Specimens

This paper presents the application of the Strain Energy Density (SED) criterion to the estimation of fracture loads on structural steel S355J2 operating at lower shelf temperatures (−196°C) and containing U-shaped notches. 24 fracture tests were performed on this material, combining 6 different notch radii: 0 mm (crack-like defect), 0.15 mm, 0.25 mm, 0.50 mm, 1.0 mm and 2.0 mm. The results obtained in cracked specimens (0 mm notch radius) were used to determine the material fracture toughness, which is an input parameter in the SED criterion, whereas the notched specimens were used to demonstrate the capacity and the limitations of the SED criterion to provide fracture load estimations in the analyzed conditions.

Elastoplastic Plane Strain Analysis of Stresses and Strains at the Notch Root

1988 ◽  
Vol 110 (3) ◽  
pp. 195-204 ◽  
Author(s):  
G. Glinka ◽  
W. Ott ◽  
H. Nowack
Keyword(s):  
Energy Density ◽  
Plane Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Equivalent Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Energy Concept ◽  
Notch Tip

For the evaluation of the local elastoplastic strains and stresses at the notch root suitable approximation formulas of sufficient accuracy are often used. In the present study the “equivalent strain energy density” concept for elastic-plastic notch strain-stress analysis has been developed. It was found that the evaluation of the strain energy density in the notch tip plastic zones does not require any input data other than the material stress-strain relation and the elastic stress concentration factor. The concept was verified on the basis of the results obtained from plane strain elastic-plastic finite element analysis using the material model after Mro´z. Comparison of the two sets of results revealed satisfactory accuracy of the equivalent strain energy concept. It was also shown that all stress and strain components in the notch tip can be calculated by complementing the method with Hencky’s equations. Neuber-based calculations were also included in the study. It was found that the energy concept was superior to Neuber’s rule, especially in the presence of high inelastic strains in the notch tip.

scholarly journals Stress-Strain Response of Cylindrical Rubber Fender under Monotonic and Cyclic Compression

Materials ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 282 ◽  
Author(s):  
Chia-Chin Wu ◽  
Yung-Chuan Chiou
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Polynomial Function ◽  
Compressive Strain ◽  
Strain Curve ◽  
Strain Range ◽  
Compression Tests ◽  
Cyclic Compression ◽  
The Relationship

The study was devoted to the observation and modeling the mechanical behaviors of a hybrid SBR/NR (Styrene-Butadiene/Natural Rubber) hybrid vulcanized rubber fender under monotonic/cyclic compression. In experimental observations of the monotonic compression tests, it was found that lateral deformation occurred on the tested fender and was more significant with increasing the extent of the compressive strain. The relationship between the transmission stress S c and the compressive strain e c was nonlinear and the absorbed strain-energy-density was increased monotonically with the increment of the compressive strain. Among all cyclic compression tests with strain controlled, the reductions in both the stress range and the absorbed strain-energy-density up to the ten-thousandth cycle were found and then both of the cyclic properties remain approximately constant in the following compression cycles. Two new properties, the softening factor and the energy reduction factor, were introduced to quantify the effect of the strain range on the extent of the reduction in stress range and that on the absorbed strain-energy-density, respectively. It was found that both of the calculated values of the new properties increase with the increment of strain range. In mathematical modeling of the relationship between the transmission stress and the compressive strain, a new approach based on energy-polynomial-function E s ( e c ) was presented and was successfully used to simulate the monotonic curve and the stable hysteresis loop curves of the tested rubber fender in compression. Essentially, the energy-polynomial-function E s ( e c ) was obtained by performing a polynomial regression on a large amount of ( e c , E s ) data. Moreover, the least-square approach was applied to determine the corresponding regression coefficients in E s ( e c ) . Clearly, the stress-polynomial-function in modeling the S c − e c curve could be obtained from the differentiation of the energy-polynomial-function with respect to the compressive strain. In addition, to provide an adequate estimation of the mechanical properties of the cylindrical rubber fender under compression, the named cyclic stress-strain curve and cyclic energy-strain curve were developed and also modeled in this study.

scholarly journals Estimation of Mode I Fracture of U-Notched Polycarbonate Specimens Using the Equivalent Material Concept and Strain Energy Density

2021 ◽  
Vol 11 (8) ◽  
pp. 3370
Author(s):  
Jafar Albinmousa ◽  
Jihad AlSadah ◽  
Muhammad A. Hawwa ◽  
Hussain M. Al-Qahtani
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Fracture Load ◽  
Image Correlation ◽  
Equivalent Material ◽  
Structural Components ◽  
Notched Specimens ◽  
Equivalent Material Concept ◽  
Material Concept

Polycarbonate (PC) has a wide range of applications in the electronic, transportation, and biomedical industries. In addition, investigation on the applicability to use PC in superstrate photovoltaic modules is ongoing research. In this paper, PC is envisioned to be used as a material for structural components in renewable energy systems. Usually, structural components have geometrical irregularities, i.e., notches, and are subjected to severe mechanical loading. Therefore, the structural integrity of these components shall consider fracture analysis on notched specimens. In this paper, rectangular PC specimens were machined with straight U-notches having different radii and depths. Eight different notch radii with a depth of 6.0 mm were tested. In addition, three notch depths with a radius of 3.5 mm were considered. Quasi-static fracture tests were performed under displacement-controlled loading with a speed of 5 mm/min. Digital image correlation technique was used to capture the strain fields for un-notched and notched specimens. It was assumed that fracture occurs at the onset of necking. The equivalent material concept (EMC) along with the strain energy density criterion (SED) were employed to estimate the fracture load. The EMC-SED combination is shown to be an effective and practical tool for estimating the fracture load of U-notched PC specimens.

scholarly journals Fatigue Failure Prediction of U-Notched ZK60 Magnesium Samples Using the Strain Energy Density Approach

Metals ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 113
Author(s):  
Jafar Albinmousa
Keyword(s):  
Energy Density ◽  
Magnesium Alloys ◽  
Fatigue Failure ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Fatigue Behavior ◽  
Cyclic Plasticity ◽  
Cyclic Tests ◽  
Notched Specimens ◽  
Structural Parts

The light weight of magnesium alloys makes them a promising material in different potential industries, such as aerospace and automobile. In addition, magnesium alloys are attractive materials for biomedical applications due to their biocompatibility with the human body. The applications of these alloys in structural parts require an understanding of their fatigue behavior because they are usually subjected to time-varying loading. Furthermore, notches are inevitable in structural parts. Geometrical discontinuities weaken structures because they act as stress raisers. Localized cyclic plasticity around notches leads to crack formation and final failure. The main objective of this research was to investigate the fatigue failure of ZK60-T5 extrusion in the presence of a notch. U-notched specimens with a diameter of 16 mm, notch radius of 1.5 mm, and notch depth of 1.5 mm were machined along the extrusion direction. Cyclic tests were performed under completely reversed cyclic loading and ambient conditions. The results obtained from the cyclic tests of the U-notched specimens were compared with those of unnotched and V-notched specimens to assess the effects of both the presence and the geometry of a notch on fatigue life. The strain energy density approach was successfully used to analyze the fatigue behavior of the U-notch specimens.

Mechanical Behavior Modeling of Hyperelastic Transversely Isotropic Materials Based on a New Polyconvex Strain Energy Function

2018 ◽  
Vol 10 (09) ◽  
pp. 1850104 ◽  
Author(s):  
D. M. Taghizadeh ◽  
H. Darijani
Keyword(s):  
Energy Density ◽  
Mechanical Behavior ◽  
Test Data ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Transversely Isotropic ◽  
Material Behavior ◽  
Isotropic Materials ◽  
Proposed Model ◽  
Transversely Isotropic Materials

In this paper, the mechanical behavior of incompressible transversely isotropic materials is modeled using a strain energy density in the framework of Ball’s theory. Based on this profound theory and with respect to physical and mathematical aspects of deformation invariants, a new polyconvex constitutive model is proposed for the mechanical behavior of these materials. From the physical viewpoint, it is assumed that the proposed model is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber–matrix interaction where each of the parts should be presented in terms of the invariants consistent with the physics of the deformation. From the mathematical viewpoint, the proposed model satisfies the fundamental postulates on the form of strain energy density, specially polyconvexity and coercivity constraints. Indeed, polyconvexity ensures ellipticity condition, which in turn provides material stability and in combination with coercivity condition, guarantees the existence of the global minimizer of the total energy. In order to evaluate the performance of the proposed strain energy density function, some test data of incompressible transverse materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and the obtained results from the proposed model. At the end, the performance of the proposed model in the prediction of the material behavior is evaluated rather than other models for two representative problems.

Damage Criteria Based on Plastic Strain Energy Intensity Under Complicated Stress State

2015 ◽  
Vol 07 (06) ◽  
pp. 1550089 ◽  
Author(s):  
Junping Shi ◽  
Xiaoshan Cao ◽  
Chao Shen
Keyword(s):  
Stress State ◽  
Energy Density ◽  
Plastic Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Energy Intensity ◽  
Yield Condition ◽  
Uniaxial Tensile ◽  
Fracture Plane ◽  
Plastic Strain Energy

In this study, total strain theory and isotropic hardening model based on Mises yield condition are used to derive the expression for plastic strain energy density under complicated stress state. The normal and shear stress distributions of a solid cylindrical bar under a combination of tensile and torsional stresses as well as the equation and integral formula for plastic strain energy density are presented. The plastic strain energy density of critical point and the plastic strain energy intensity on the fracture plane of different materials under several typical stress states are obtained by measuring the fracture data of different materials. With the plastic strain energy intensity as the failure parameter, uniaxial tensile experiments were conducted to measure the final plastic strain energy intensity of the failure section. The plastic strain energy intensity failure criteria of the material under complex stress state are established. Combined tension–torsion tests were conducted on two types of materials, LC9 and LY12, to verify the validity and applicability of the criteria.

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