The Three Controlling Modes of Failure in Homogeneous and Isotropic Materials With Proof Thereof Through Critical Plane Stress Conditions

2021 ◽  
Vol 89 (1) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Plane Stress ◽  
Entire Range ◽  
Three Dimensional ◽  
Stress Conditions ◽  
Teaching Tool ◽  
Critical Plane ◽  
Modes Of Failure ◽  
Failure Theory ◽  
Mode Of Failure ◽  
Materials Failure

Abstract The recently developed general materials failure theory is specialized to the two-dimensional state of plane stress. It takes a form that is virtually no more involved than that of the Mises criterion. Yet it remains applicable to the entire range of materials types and thus retains that generality. The Mises form has absolutely no capability for generality. This plane stress form of the new failure theory reveals the existence of three independent modes and mechanisms of failure, not two, not four, purely three. The Mises criterion has one mode of failure. These three modes of failure are fully examined. It is verified that these modes of failure under plane stress conditions are exactly the same as those operative in the three-dimensional case. The simple plane stress form of the failure theory has major appeal and likely use as a teaching tool to introduce failure and to help de-mystify the vitally important general subject of materials failure.

scholarly journals The ductile/brittle transition provides the critical test for materials failure theory

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170817 ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Uniaxial Tension ◽  
Brittle Failure ◽  
Functional Form ◽  
Three Dimensional ◽  
Failure Surface ◽  
Critical Test ◽  
Full Account ◽  
Brittle Transition ◽  
Failure Theory ◽  
Materials Failure

It is reasoned that any materials failure theory that claims generality must give full account of ductile versus brittle failure behaviour. Any such proposed theory especially must admit the capability to generate the ductile/brittle transition. A derivation of the failure surface orientations from a particular isotropic materials failure theory reveals that uniaxial tension has its ductile/brittle transition at T / C  = 1/2, where T and C are the uniaxial strengths. Between this information and the corresponding ductile/brittle transition in uniaxial compression it becomes possible to derive the functional form for the fully three-dimensional ductile/brittle transition. These same general steps of verification must be fulfilled for any other candidate general failure theory.

ProgramCRYC3Dfor geometric computing in crystallography

2008 ◽  
Vol 41 (2) ◽  
pp. 479-480 ◽  
Author(s):  
Ludmila Urzhumtseva ◽  
Alexandre Urzhumtsev
Keyword(s):  
Computer Program ◽  
Three Dimensional ◽  
Teaching Tool ◽  
Online Help ◽  
Principal Mode ◽  
Geometric Characteristics ◽  
Simple Program ◽  
Or Groups ◽  
Geometric Objects ◽  
Everyday Work

The computer programCRYC3Dworks with three-dimensional crystallographic geometric objects or groups of them and calculates their basic geometric characteristics by a simple click in the menu. In particular, this includes vector operations in both direct and reciprocal spaces and cell transformations. Collecting basic crystallographic operations in a single and simple program helps crystallographers to avoid looking for `fast-and-dirty' scripts or using large and unwieldy packages and may be useful in everyday work. When running the program in its principal mode, macro-operations are accompanied by a list of elementary geometric operations. This feature, together with the presence of a single-command mode and online help, may be useful also as a teaching tool.

scholarly journals Numerical Analyses on the Stability of a Deep Coalmine Roadway Passing through a Fault Zone: A Case Study of the Gugui Coalfield in China

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2114
Author(s):  
Yongshui Kang ◽  
Congcong Hou ◽  
Jingyi Liu ◽  
Zhi Geng ◽  
Jianben Chen ◽  
...  
Keyword(s):  
Fault Zone ◽  
Distinct Element ◽  
Three Dimensional ◽  
Tectonic Stress ◽  
Three Dimensional Model ◽  
Support Strategy ◽  
Failure Theory ◽  
Calculation Results ◽  
Pass Through ◽  
The Stability

Massive deformation often occurs when deep coalmine roadways pass through a fault zone due to the poor integrity of rock mass and high tectonic stress. To study deformation characteristics of the surrounding rock in the fault zone of a coalmine, a roadway passing through the FD1041 fault zone in China’s Gugui coalfield was investigated in this research. The geo-stress characteristics of this fault zone were analyzed based on the Mohr failure theory. Furthermore, a three-dimensional model for the experimental roadway in the FD1041 fault zone was built and calculated by a numerical program based on the distinct element method. Stability conditions of the roadway, using several types of support methods, were calculated and compared. Calculation results indicated that pre-grouting provides favorable conditions for the stability of a roadway in a fault zone. Finally, an optimized support strategy was proposed and implemented in the experimental roadway. Monitored results demonstrated that the optimized support strategy is appropriate for this fault zone.

Thermal Stresses in Moderately Thick Elastic Plates

1959 ◽  
Vol 26 (3) ◽  
pp. 432-436
Author(s):  
B. E. Gatewood
Keyword(s):  
Temperature Gradient ◽  
Plane Stress ◽  
Thermal Stresses ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Elastic Plates ◽  
Plate Length ◽  
Moderately Thick Plates ◽  
Thick Elastic Plates ◽  
Thickness Variable

Abstract The three-dimensional stresses in the plate are investigated without using the plane-stress or plane-strain assumptions, the thickness of the plate being limited so that the normal stress in the thickness direction can be taken as a polynomial in the thickness variable. The temperature is taken as a polynomial in the thickness variable but with relatively large, though restricted, gradients with respect to the co-ordinates of the plane of the plate. For the case of the temperature constant in thickness variable, the stresses in the plane of the plate are presented as the plane-stress solution plus correcting terms due to the plate thickness, where the correcting terms involve the product of the temperature gradient and the ratio of the plate thickness to the plate length in the direction of the temperature gradient. In many cases the corrections are small even for moderately thick plates.

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