Proof of the Splitting Mode of Compressive Brittle Failure and Integration With General Failure Theory

2019 ◽  
Vol 86 (9) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Uniaxial Compression ◽  
Special Interest ◽  
Brittle Failure ◽  
Difficult Problem ◽  
Theoretical Treatment ◽  
Isotropic Materials ◽  
Failure Theory ◽  
Mode Of Failure ◽  
Technical Capability

The problem of special interest is the nature of the mode of failure in uniaxial compression at the brittle limit. This problem is known by observation to undergo a splitting mode of failure. The present work gives a full theoretical treatment and proof for this mode of failure. The general failure theory of Christensen for isotropic materials provides the basis for the derivation. The solution demonstrates the depth of technical capability that is required from the failure theory to treat such a classically difficult problem.

The Theoretical Measure of the Ductility of Failure for All Isotropic Materials in All States of Stress1

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Stress State ◽  
Brittle Failure ◽  
Failure Stress ◽  
Isotropic Materials ◽  
Failure Theory

The ductile/brittle failure theory for homogeneous and isotropic materials is extended to give a rational and mathematically rigorous measure for the ductility of failure. This new failure number methodology is completely developed and proved to be valid and general. It applies to all isotropic materials as subjected to any and all states of stress. Not only does the failure theory predict the safety or failure for any given stress state, it then projects the quantitative ductility level for the failure stress state. Many important examples are given with detailed interpretations of the results and with guides for general usage.

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.

The Failure Theory for Isotropic Materials: Proof and Completion

2019 ◽  
Vol 87 (5) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Brittle Failure ◽  
Ductile Failure ◽  
Isotropic Materials ◽  
Failure Theory ◽  
History Of ◽  
Failure Properties ◽  
Complete Form ◽  
The Many ◽  
Entire Theory

Abstract This work represents the completion of the many developments in recent years on failure theory for homogeneous and isotropic materials. Presented here is the resulting failure formalism in final and technically complete form. Significant further results are also given for the verification of the failure formalism. The scope of this paper goes from the history of misguided failure theory investigations right up to the present final tested forms ready for applications. For every predicted failure level in terms of the stresses, there is an accompanying ductility level. This ranges from brittle failure up to fully ductile failure. The entire theory is calibrated by only two specified parameters (failure properties). Nothing else is needed. The seemingly interminable, actually centuries long search for the missing theory of failure has finally been brought to a resolute and successful conclusion.

scholarly journals Mechanical Properties and Acoustic Emission Characteristics of Karst Limestone under Uniaxial Compression

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jianxun Chen ◽  
Qingsong Wang ◽  
Jiaqi Guo ◽  
Yanbin Luo ◽  
Yao Li ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Acoustic Emission ◽  
Water Content ◽  
Uniaxial Compression ◽  
Wave Velocity ◽  
Brittle Failure ◽  
Shear Failure ◽  
Testing Machine ◽  
Natural State ◽  
Saturated State

Firstly, I-RPT ultrasonic detector was used to test the wave velocity of karst limestone with different initial microstructure and water content. Then, RMT-150B rock testing machine and DS2-16B acoustic emission system were used to test the acoustic emission (AE) under uniaxial compression. Mechanical properties and AE characteristics were obtained during rock failure. The detailed relationship between stress-strain and AE characteristics was studied in this paper. Research results indicated the following: (1) For samples with many primary fissures and defects, wave velocity in dry state was larger than that in its natural state. From natural state to saturated state, the wave velocity tended to increase. For samples with good integrity, wave velocity increased with increasing of water content. (2) In the dry state, the samples presented tension failure. In saturated state, the samples presented tension-shear failure. For samples with cracks and good integrity, samples showed brittle failure. For samples with many corrosion pores which showed ductile damage under natural and saturated state, the spalling phenomenon was enhanced under saturated state. (3) With increasing of water content, the peak stress and AE peak reduced dramatically. In brittle failure, AE peak could be considered a sign of failure. In ductile failure, AE activity decreased gradually with the decrease of stress. (4) The mechanical properties and AE characteristics corresponding to four main fracture propagation types were also discussed.

scholarly journals A Comprehensive Theory of Yielding and Failure for Isotropic Materials

2007 ◽  
Vol 129 (2) ◽  
pp. 173-181 ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Stress State ◽  
Brittle Failure ◽  
Three Dimensional ◽  
Present Theory ◽  
Full Density ◽  
Isotropic Materials ◽  
Comprehensive Theory ◽  
General Material ◽  
Ductile Behavior ◽  
Limiting Case

A theory of yielding and failure for homogeneous and isotropic materials is given. The theory is calibrated by two independent, measurable properties and from those it predicts possible failure for any given state of stress. It also differentiates between ductile yielding and brittle failure. The explicit ductile-brittle criterion depends not only upon the material specification through the two properties, but also and equally importantly depends upon the type of imposed stress state. The Mises criterion is a special (limiting) case of the present theory. A close examination of this case shows that the Mises material idealization does not necessarily imply ductile behavior under all conditions, only under most conditions. When the first invariant of the yield/failure stress state is sufficiently large relative to the distortional part, brittle failure will be expected to occur. For general material types, it is shown that it is possible to have a state of spreading plastic flow, but as the elastic-plastic boundary advances, the conditions for yielding on it can change over to conditions for brittle failure because of the evolving stress state. The general theory is of a three-dimensional form and it applies to full density materials for which the yield/failure strength in uniaxial tension is less than or at most equal to the magnitude of that in uniaxial compression.

scholarly journals Scapholunate Ligament Internal Brace 360 Tenodesis (SLITT) Procedure: A Biomechanical Study

2018 ◽  
Vol 08 (03) ◽  
pp. 250-254
Author(s):  
Sanjeev Kakar ◽  
Ryan M. Greene ◽  
Janet Denbeigh ◽  
Andre Van Wijnen
Keyword(s):  
Surgical Techniques ◽  
Maximum Load ◽  
Difficult Problem ◽  
Biomechanical Study ◽  
Mode Of Failure ◽  
Load To Failure ◽  
Internal Brace ◽  
Fresh Frozen ◽  
Prolonged Immobilization ◽  
Ligament Disruption

Background Twelve paired fresh frozen cadaveric wrists were randomized to a 360-degree tenodesis repair group or the 360-degree tenodesis repair with an internal brace (suture tape) construct. Case Description The specimens were preloaded to 5 N and subsequently biomechanically loaded to failure, at a rate of 0.1 mm/s on a jig that allowed for axial load. The maximum load and mode of failure were recorded. Load to failure in the 360 tenodesis group with internal brace was 283.47 ± 100.25 N, compared with the 360 tenodesis group only, whose yield strength was 143.61 ± 90.54 N. The mode of failure within the internal brace construct was either through knot slippage, graft disruption, or bone separation from strength testing construct. The 360 tenodesis group tended to fail via graft slippage or graft rupture. Literature Review The management of scapholunate instability can be a difficult problem to treat. Traditionally, many of the surgical reconstructions have focused upon dorsal ligament reconstruction with Kirschner (K) wire fixation. This results in prolonged immobilization of the wrist with varied outcomes, in part due to the multiaxial instability that may persist due to concomitant volar ligament disruption. To address this instability, surgical techniques have been devised that address both the volar and dorsal ligament injuries. Clinical Relevance Scapholunate reconstruction with a 360-degree tenodesis and internal brace augmentation (SLITT procedure) provided superior biomechanical stability than tenodesis alone.

On the Eigenstrain Problem of a Spherical Inclusion With an Imperfectly Bonded Interface

1996 ◽  
Vol 63 (4) ◽  
pp. 877-883 ◽  
Author(s):  
Z. Zhong ◽  
S. A. Meguid
Keyword(s):  
Spherical Inclusion ◽  
Normal Displacement ◽  
Theoretical Treatment ◽  
Interfacial Condition ◽  
Isotropic Materials ◽  
Interfacial Sliding ◽  
Bonded Interface ◽  
Special Cases ◽  
Normal Separation ◽  
Displacement Jumps

This article provides a comprehensive theoretical treatment of the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface. Both tangential and normal discontinuities at the interface are considered and a linear interfacial condition, which assumes that the tangential and the normal displacement jumps are proportional to the associated tractions, is adopted. The solution to the corresponding eigenstrain problem is obtained by combining Eshelby’s solution for a perfectly bonded inclusion with Volterra’s solution for an equivalent Somigliana dislocation field which models the interfacial sliding and normal separation. For isotropic materials, the Burger’s vector of the equivalent Somigliana dislocation is exactly determined; the solution is explicitly presented and its uniqueness demonstrated. It is found that the stresses inside the inclusion are not uniform, except for some special cases.

Benjamin Lees's String Quartet Concerto

Tempo ◽  
1967 ◽  
pp. 21-25
Author(s):  
Niall O'Loughlin
Keyword(s):  
String Quartet ◽  
Special Interest ◽  
Kansas City ◽  
Difficult Problem

Benjamin Lees's Concerto for string quartet and orchestra was written on commission for the Kansas City Philharmonic Orchestra, and was first performed by them under the conductor Hans Schwieger, with the Paganini Quartet as soloists, in January 1965. The unusual nature of the work arose out of the desire of Mrs. Louis Sosland who commissioned it, to help the Kansas orchestra while also continuing to foster the art of the string quartet, which was her own special interest. Lees, whose output includes highly successful works in both concerto and string quartet media, responded with a work which solves the difficult problem of combining the two with characteristic artistic mastery and inventiveness.

Failure Mechanics—Part II: The Central and Decisive Role of Graphene in Defining the Elastic and Failure Properties for all Isotropic Materials

2014 ◽  
Vol 81 (11) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Elasticity Theory ◽  
Three Dimensional ◽  
Decisive Role ◽  
Common Belief ◽  
Failure Mechanics ◽  
Isotropic Materials ◽  
Failure Theory ◽  
Failure Properties ◽  
2D Elasticity

Continuing from Part I (Christensen, 2014, “Failure Mechanics—Part I: The Coordination Between Elasticity Theory and Failure Theory for all Isotropic Materials,” ASME J. Appl. Mech., 81(8), p. 081001), the relationship between elastic energy and failure specification is further developed. Part I established the coordination of failure theory with elasticity theory, but subject to one overriding assumption: that the values of the involved Poisson's ratios always be non-negative. The present work derives the physical proof that, contrary to fairly common belief, Poisson's ratio must always be non-negative. It can never be negative for homogeneous and isotropic materials. This is accomplished by first probing the reduced two-dimensional (2D) elasticity problem appropriate to graphene, then generalizing to three-dimensional (3D) conditions. The nanomechanics analysis of graphene provides the key to the entire development. Other aspects of failure theory are also examined and concluded positively. Failure theory as unified with elasticity theory is thus completed, finalized, and fundamentally validated.

Failure Mechanics—Part I: The Coordination Between Elasticity Theory and Failure Theory for all Isotropic Materials

2014 ◽  
Vol 81 (8) ◽  
Author(s):  
Richard M. Christensen
Keyword(s):  
Mechanical Behavior ◽  
Elasticity Theory ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Poisson's Ratio ◽  
Failure Mechanics ◽  
Isotropic Materials ◽  
Intimate Connection ◽  
Failure Theory ◽  
Theory Failure

Failure mechanics is comprised of the failure theory for homogeneous and isotropic materials along with all of its implications and applications. The present failure theory is found to have an intimate connection with elasticity behavior even though plasticity may also transpire. This becomes apparent and useful when the classical theory of elasticity is renormalized to give a simpler and more transparent (but still exact) formalism. The connection or coordination between elasticity and failure then explicitly occurs through the use of the renormalized Poisson's ratio to characterize the ductility of failure. With this unification of failure theory and elasticity theory, failure mechanics can be extended to explain other anomalous aspects of mechanical behavior and prepare it for applications.

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