Revisiting Failure of Brittle Materials

2021 ◽  
Author(s):  
Young W. Kwon
Keyword(s):  
Stress Gradient ◽  
Brittle Materials ◽  
Local Stress ◽  
Failure Criteria ◽  
Material Failure ◽  
Failure Strength ◽  
Local Point ◽  
Load Carrying ◽  
Gradient Condition ◽  
Circular Notch

Abstract Failures of isotropic brittle materials were revisited to find out whether there are unified failure criteria which can be applied to a load-carrying structural component made of a brittle material regardless of whether the component has a crack, a circular notch, or neither of these. To this end, a set of failure criteria were considered to determine failure of a local point which may be located at the crack tip, a notch tip, or any other location. The proposed criteria consist of two conditions, of which both must be satisfied for failure to occur. The first condition is that the local stress must not be lower than the failure strength of the material. The second condition is the stress-gradient condition. Even if the stress at a local point far exceeds the failure strength of the material, failure will not initiate until the stress gradient condition is satisfied. Four different examples cases were presented to explain the proposed failure concept.

A Teaching Note on Failure Criteria and Failure Surfaces for Ductile and Brittle Materials

1994 ◽  
Vol 22 (1) ◽  
pp. 1-13 ◽  
Author(s):  
G. S. Schajer
Keyword(s):  
Isotropic Material ◽  
Three Dimensional ◽  
Brittle Materials ◽  
Failure Criteria ◽  
Material Failure ◽  
Stress Space ◽  
Ductile Materials ◽  
Basic Concepts ◽  
Multiaxial Loadings

This note discusses some basic concepts underlying isotropic material failure criteria under multiaxial loadings. It also describes the shapes and features of the associated failure surfaces in three-dimensional stress space. Failure criteria for ductile materials are first reviewed. They are then generalized so that they may also be applied to brittle materials. The relationships among the various failure criteria, the shapes and characteristics of the associated failure surfaces, and the special features of physically acceptable isotropic failure criteria are then considered.

scholarly journals A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler– Pister and Willam–Warnke

2020 ◽  
Vol 476 (2238) ◽  
pp. 20190861 ◽  
Author(s):  
Oliver Giraldo-Londoño ◽  
Glaucio H. Paulino
Keyword(s):  
Topology Optimization ◽  
Optimization Problems ◽  
Local Stress ◽  
Stress Constraints ◽  
Failure Criteria ◽  
Yield Function ◽  
Material Failure ◽  
Local Material ◽  
Gradient Based ◽  
Von Mises

An interesting, yet challenging problem in topology optimization consists of finding the lightest structure that is able to withstand a given set of applied loads without experiencing local material failure. Most studies consider material failure via the von Mises criterion, which is designed for ductile materials. To extend the range of applications to structures made of a variety of different materials, we introduce a unified yield function that is able to represent several classical failure criteria including von Mises, Drucker–Prager, Tresca, Mohr–Coulomb, Bresler–Pister and Willam–Warnke, and use it to solve topology optimization problems with local stress constraints. The unified yield function not only represents the classical criteria, but also provides a smooth representation of the Tresca and the Mohr–Coulomb criteria—an attribute that is desired when using gradient-based optimization algorithms. The present framework has been built so that it can be extended to failure criteria other than the ones addressed in this investigation. We present numerical examples to illustrate how the unified yield function can be used to obtain different designs, under prescribed loading or design-dependent loading (e.g. self-weight), depending on the chosen failure criterion.

STUDY ON FATIGUE BEHAVIOR OF STRENGTHENED NON-LOAD-CARRYING CRUCIFORM WELDED JOINTS USING CARBON FIBER SHEETS

2012 ◽  
Vol 12 (01) ◽  
pp. 179-194 ◽  
Author(s):  
TAO CHEN ◽  
QIAN-QIAN YU ◽  
XIANG-LIN GU ◽  
XIAO-LING ZHAO
Keyword(s):  
Stress Concentration ◽  
Carbon Fiber ◽  
Welded Joints ◽  
Failure Modes ◽  
Fatigue Behavior ◽  
Local Stress ◽  
Fatigue Loading ◽  
Cfrp Sheets ◽  
Load Carrying ◽  
Weld Toe

This paper reports an experimental study on the use of carbon fiber-reinforced polymer (CFRP) sheets to strengthen non-load-carrying cruciform welded joints subjected to fatigue loading. Failure modes and corresponding fatigue lives were recorded during tests. Scatter of test results was observed. Thereafter, a series of numerical analyses were performed to study the effects of weld toe radius, the number of CFRP layers and Young's modulus of reinforced materials on local stress concentration at a weld toe. It was found that fatigue life of such welded connections can be enhanced because of the reduction of stress concentration caused by CFRP strengthening. Parametric study indicates that the weld toe radius and the amount of CFRP are the key parameters influencing the stress concentration factors and stress ranges of the joint. Enhancement of modulus for adhesive and CFRP sheets can also be beneficial to the fatigue performance to some extent.

Application of the Deformation Theory of Plasticity for Determining Elastoplastic Stress and Strain Concentration Factors

1976 ◽  
Vol 98 (4) ◽  
pp. 1152-1156 ◽  
Author(s):  
J. P. Eimermacher ◽  
I.-Chih Wang ◽  
M. L. Brown
Keyword(s):  
Deformation Theory ◽  
Analytical Data ◽  
Local Stress ◽  
Failure Criteria ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Strain Concentration ◽  
Theory Of Plasticity ◽  
Concentration Factors ◽  
Von Mises

The deformation theory of plasticity is considered as a means for obtaining a solution to the problem of calculating stress and strain concentration factors at geometric discontinuities where the local stress state exceeds the yield strength of the material. Through the use of the Hencky-Nadai constitutive law and the Von Mises failure criteria, the elastoplastic element stiffness matrix is derived for a plane stress triangular plate element. An elastoplastic solution is arrived at by considering direct-iterative and finite element techniques. Verification of the analytical results is obtained by considering a numerical example and comparing the calculated results with published experimental and analytical data.

Dynamical Fracture Instabilities Due to Local Hyperelasticity at Crack Tips

2006 ◽  
Vol 929 ◽  
Author(s):  
Markus J. Buehler ◽  
Huajian Gao
Keyword(s):  
Large Scale ◽  
Brittle Materials ◽  
Crack Tip ◽  
Local Stress ◽  
Nonlinear Material ◽  
Physical Reason ◽  
Shear Wave Speed ◽  
Linear Elastic ◽  
Strongly Nonlinear ◽  
Wide Range

ABSTRACTWhen materials break and cracks propagate, bonds between atoms are broken generating two new material surfaces. Most existing theories of fracture assume a linear elastic stress-strain law. However, the relation between stress and strain in real solids is strongly nonlinear due to large deformation near a moving crack tip, a phenomenon referred to as hyperelasticity or nonlinear elasticity. Cracks moving at low speeds create atomically flat mirror-like surfaces, whereas cracks at higher speeds leave misty and hackly fracture surfaces. This change in fracture surface morphology is a universal phenomenon found in a wide range of different brittle materials, but the underlying physical reason has been debated over an extensive period. Using massively parallel large-scale atomistic simulations employing a new, simple atomistic material model allowing a systematic transition from linear elastic to strongly nonlinear material behaviors, we show that hyperelasticity can play a governing role in dynamical crack tip instabilities in fracture of brittle materials. We report a generalized model that treats the instability problem as a competition between different mechanisms controlled by local stress field and local energy flow near the crack tip. Our results indicate that the fracture instabilities do not only appear in defected materials, but instead are an intrinsic phenomenon of dynamical fracture. Our findings help to explain controversial experimental and computational results, including experimental observation of crack propagation at speeds beyond the shear wave speed in rubber-like materials.

scholarly journals Design of Composite I-Beam Section to Prevent Web-Flange Junction Failure and Improving Its Axial Load Carrying Capacity

2019 ◽  
Vol 9 (1) ◽  
pp. 2373-2380
Keyword(s):  
Glass Fiber ◽  
Carrying Capacity ◽  
Failure Strength ◽  
Load Carrying Capacity ◽  
Flat Plates ◽  
Element Analysis ◽  
Bath Solution ◽  
Load Carrying ◽  
Acidic Bath ◽  
The Web

Most of the chemical industries are used with Polyurethane (PU) coated steel sample which is found that some chemical reaction and rusted in acidic bath solution becomes a problem in industry. For such problems composite materials can be of good solution which does not possess any reaction with working fluids (acids in our case). With composites there is complexity of manufacturing and high cost involvement, so as to avoid those simplified approach is used to get Flat plates made of Glass fiber reinforced in epoxy which is best solution for any acidic bath as it possesses high resistance to any reaction with itself. Glass fiber plates are cut into the size of dimension and with the help of adhesives joint the WFJ of I-Beam, there are two different types of adhesives used, araldite 2015 and Hundsman araldite are used. The hundsman araldite is found to get better performance of Web-Flange junction (WFJ) joint. Finite element analysis (FEA) is used to get initial validation and further it’s observed that Hundsman araldite failure strength on the web-flange junction is better. Also, additional cleat used with 4 mm, 12 mm for increasing the Web-Flange junction (WFJ) area to improve the Load carrying capacity of the Beam. The experimental analysis results clearly indicate that the emersion of the reinforced epoxy glass-fiber in the acidic bath solution for a certain period, there is no any reaction formed in the acidic bath and improved the behavior of the specimen. Results from FEA and experimental test have shown good correlations are obtained with improvement of failure strength on WFJ

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