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plane strain

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Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 30 November 2013
DOI: 10.31399/asm.tb.uhcf3.t53630257
EISBN: 978-1-62708-270-9
... Abstract Fracture mechanics is a well-developed quantitative approach to the study of failures. This chapter discusses fracture toughness and fracture mechanics, linear-elastic fracture mechanics, and modes of loading. The discussion also covers plane strain and stress and crack growth kinetics...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040091
EISBN: 978-1-62708-300-3
..., covering basic principles, implementation, and advantages and disadvantages in various applications. axisymmetric upsetting finite element method forging plane-strain slab method upperbound method References [Altan et al., 1979] Altan T. , Lahoti G.D...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040017
EISBN: 978-1-62708-300-3
... distribution of velocity components and strain rates. It describes the conditions associated with homogeneous deformation in a frictionless upset forging and explains how they can also be obtained using engineering and true stress-strain curves. flow stress plane stress plastic deformation strain rate...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smff.t53400027
EISBN: 978-1-62708-316-4
... uniformly over the principal axes, the material is isotropic in the cross-sectional plane. For anisotropic materials, however, the cross section will reduce nonuniformly, such that for a strip, for instance, the thickness strain will be different from the width strain. Equation 3.16 is another reason...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 June 2008
DOI: 10.31399/asm.tb.emea.t52240221
EISBN: 978-1-62708-251-8
... failure transitions to a brittle failure. The discussion then covers the Griffith theory of brittle fracture and the formulation of fracture mechanics. Procedures for determination of the plane-strain fracture toughness are subsequently covered. Finally, the chapter describes the effects of...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540411
EISBN: 978-1-62708-309-6
... Abstract This appendix provides tensile property data for titanium alloys and castings and plane-strain fracture toughness data for Ti-6Al-4V castings. alpha-beta titanium alloys beta titanium alloys titanium castings plane-strain fracture toughness tensile properties LIMITED...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540169
EISBN: 978-1-62708-309-6
... rate, the use of fracture indices and failure criteria, and the ramifications of crack-tip plasticity in ductile and brittle fractures. It goes on to describe the different types of plain-strain and plane-stress fracture toughness, explaining how they are measured and how they are influenced by...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540001
EISBN: 978-1-62708-309-6
... the cutting plane and A is the cross-sectional area of the rod. Therefore, in equilibrium: (Eq 1.1b) σ = P / A If we gradually increase the strain of a Hooke solid, the stress is also increased proportionally. The relation of traction to strain is a linear line as shown in Fig...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 2017
DOI: 10.31399/asm.tb.sccmpe2.t55090367
EISBN: 978-1-62708-266-2
... “ Standard Test Method for Plane-Strain Fracture Toughness Testing of Metallic Materials ,” E 399, Annual Book of ASTM Standards , Vol 03.01 , ASTM 17.30 Hauser J.A. II , Judy R.W. Jr. , and Crooker T.W. , “ Draft Standard Method of Test for Plane-Strain Stress-Corrosion-Cracking...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smff.t53400053
EISBN: 978-1-62708-316-4
... ⁡ = σ 1 = σ ¯ 3 The Tresca yield criterion gives: σ ¯ = 2 σ 1 and τ max ⁡ = σ 1 = σ ¯ 2 In the plane strain (point E), the two yield criteria exhibit different yield stresses. With the...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2012
DOI: 10.31399/asm.tb.ffub.t53610101
EISBN: 978-1-62708-303-4
... methods and specimen configurations that have been developed to measure the toughness of various materials. In this chapter, five of the more common methods are covered: impact ductile-to-brittle transition temperature testing, drop-weight testing, plane-strain fracture toughness, J -integral, and crack...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smfpa.t53500019
EISBN: 978-1-62708-317-1
... G.L. , and Altan T. , Mathematical Modeling of Plane-Strain Bending of Sheet and Plate , J. Mater. Process. Technol. , Vol 39 , 1993 , p 279 – 304 10.1016/0924-0136(93)90164-2 2.2 Hill R. , The Mathematical Theory of Plasticity , Oxford , London , 1950 , p 288 – 294...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040051
EISBN: 978-1-62708-300-3
... its microstructure and depends on shear strain rate, strain, and deformation temperature. This yield criterion can easily be described by the aid of Mohr circles for stresses. Figure 5.5 shows a Mohr circle that represents the stresses in a plane whose coordinate axes are chosen to be the shear...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.tb.scm.t52870421
EISBN: 978-1-62708-314-0
... 2 − 2 m n − 2 m n 2 m n m 2 − n 2 ] { ε xx ε yy γ xy } For a thin isotropic material in plane stress loading ( Fig. 16.4a ), the stress-strain relationships within the elastic range are: (Eq 16.5...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2012
DOI: 10.31399/asm.tb.ffub.t53610147
EISBN: 978-1-62708-303-4
... Crack length as a function of cycles. Source: Ref 1 Fig. 41 Crack propagation curve for fatigue loading. Source: Ref 1 Because the zone ahead of the crack that experiences cyclic plasticity (i.e., the fatigue plastic zone) is very small, plane-strain conditions can develop even for...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 2015
DOI: 10.31399/asm.tb.spsp2.t54410213
EISBN: 978-1-62708-265-5
... segregation of the interstitial atoms to the elastic strain fields of dislocations. For example, edge dislocations, where the lattice discontinuity is a line extending along the edge of an incomplete plane of atoms, have a tensile strain field below that edge and can accommodate interstitial atoms more...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540121
EISBN: 978-1-62708-309-6
... failure (whether or not there is a runout in the S-N curve) is quite common. At low strain amplitudes (long-life fatigue), a material with higher tensile strength normally has better resistance to slip. Because failure due to monotonic loading or fatigue begins with slip of crystallographic planes...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smff.t53400105
EISBN: 978-1-62708-316-4
... key process parameters including the draw ratio, material properties, geometry, interface conditions, equipment operating speed, and tooling. It then walks through the steps involved in predicting stress, strain, and punch force using the slab method and finite element analysis and presents the...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2013
DOI: 10.31399/asm.tb.ahsssta.t53700135
EISBN: 978-1-62708-279-2
... Abstract This chapter briefly discusses the characteristics of mechanical twins and stacking faults in close-packed planes. It provides an overview of the composition, microstructures, thermodynamics, processing, deformation mechanism, mechanical properties, formability, and special attributes...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 2017
DOI: 10.31399/asm.tb.sccmpe2.t55090333
EISBN: 978-1-62708-266-2
... Abstract Amorphous alloys, because of their lack of crystallographic slip planes, are assumed to be insensitive to the selective corrosion attack that causes stress-corrosion cracking (SCC) in crystalline alloys. However, under certain conditions, melt-spun amorphous alloys have proven...