scholarly journals Correction to ‘The ductile/brittle transition provides the critical test for materials failure theory’

2018 ◽  
Vol 474 (2211) ◽  
pp. 20180114
Author(s):  
Richard M. Christensen
Keyword(s):  
Critical Test ◽  
Brittle Transition ◽  
Failure Theory ◽  
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.

Evaluation of Ductile/Brittle Failure Theory and Derivation of the Ductile/Brittle Transition Temperature

2015 ◽  
Vol 83 (2) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Transition Temperature ◽  
Brittle Failure ◽  
Evaluation Process ◽  
Isotropic Materials ◽  
Brittle Transition ◽  
Failure Theory ◽  
Ductile Brittle Transition Temperature ◽  
Brittle Transition Temperature ◽  
Materials Failure

A recently developed ductile/brittle theory of materials failure is evaluated. The failure theory applies to all homogeneous and isotropic materials. The determination of the ductile/brittle transition is an integral and essential part of the failure theory. The evaluation process emphasizes and examines all aspects of the ductile versus the brittle nature of failure, including the ductile limit and the brittle limit of materials' types. The failure theory is proved to be extraordinarily versatile and comprehensive. It even allows derivation of the associated ductile/brittle transition temperature. This too applies to all homogeneous and isotropic materials and not just some subclass of materials' types. This evaluation program completes the development of the failure theory.

Mechanisms and measures for the ductility of materials failure

2020 ◽  
Vol 476 (2239) ◽  
pp. 20190719
Author(s):  
Richard M. Christensen
Keyword(s):  
Brittle Failure ◽  
Periodic Table ◽  
Operational Definition ◽  
Atomic Scale ◽  
Brittle Transition ◽  
Bond Stretching ◽  
Bond Bending ◽  
Materials Failure

An operational definition for the ductility of failure is given. Many examples illustrate the procedure for specific applications. The ductile/brittle transition is an integral part of the formalism. Further applications are made to the solids forming elements in the Periodic Table. The cases of graphene and diamond are used to verify the procedure. Bond bending and bond stretching are shown to provide an atomic scale criterion for ductile versus brittle failure behaviours.

Perspective on Materials Failure Theory and Applications

2016 ◽  
Vol 83 (11) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Failure Criteria ◽  
Research Progress ◽  
Theory Formulation ◽  
Failure Theory ◽  
Long Time ◽  
History Of ◽  
Materials Failure ◽  
Recent Research Progress

The history of developing failure criteria is briefly examined. The cumulative result is found to be completely unsatisfactory and extremely misleading, to the point of crisis. The long time blockage of the materials failure field has had serious and retarding effects on all related technical areas that are dependent on reliable failure projections. A new and rationally different approach to failure theory formulation is outlined and fully documented. After summarizing recent research progress, a program for the recovery and revitalization of the field is given.

Materials Failure Theory and Applications, Change Is Coming

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Failure Criteria ◽  
The State ◽  
Isotropic Materials ◽  
Current State ◽  
Failure Theory ◽  
The Future ◽  
Materials Failure ◽  
The Many ◽  
State Of The Field

This overview/survey assesses the state of the discipline for the failure of homogeneous and isotropic materials. It starts with a quick review of the many historical but unsuccessful failure investigations. Then, it outlines the dysfunctional current state of the field for failure criteria. Finally, it converges toward the technical prospects that can and very likely will bring much needed change and progress in the future.

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 Homogeneous and Isotropic Materials Failure Theory: A Critical Appraisal

2021 ◽  
pp. 1-6
Author(s):  
Richard M. Christensen
Keyword(s):  
Critical Appraisal ◽  
Isotropic Materials ◽  
Failure Theory ◽  
Critical Detail ◽  
Materials Failure

Abstract The historical status of failure theory is surveyed and found to be close to chaotic. Abandoning that source, the constructive associations and operations that must be required in order to form a viable theory of materials failure are examined in critical detail. The consequent failure theory has been established and its future is discussed.

Real-time cryo-deformation of polypropylene and impact-modified polypropylene in the transmission electron microscope

1993 ◽  
Vol 51 ◽  
pp. 892-893
Author(s):  
Robert C. Cieslinski ◽  
H. Craig Silvis ◽  
Daniel J. Murray
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Failure Mechanisms ◽  
Brittle Transition ◽  
Molded Part ◽  
Transmission Electron ◽  
Solvent Cast ◽  
The Impact ◽  
Annealed Copper ◽  
Dynamic Plane

An understanding of the mechanical behavior polymers in the ductile-brittle transition region will result in materials with improved properties. A technique has been developed that allows the realtime observation of dynamic plane stress failure mechanisms in the transmission electron microscope. With the addition of a cryo-tensile stage, this technique has been extented to -173°C, allowing the observation of deformation during the ductile-brittle transition.The technique makes use of an annealed copper cartridge in which a thin section of bulk polymer specimen is bonded and plastically deformed in tension in the TEM using a screw-driven tensile stage. In contrast to previous deformation studies on solvent-cast films, this technique can examine the frozen-in morphology of a molded part.The deformation behavior of polypropylene and polypropylene impact modified with EPDM (ethylene-propylene diene modified) and PE (polyethylene) rubbers were investigated as function of temperature and the molecular weight of the impact modifier.

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