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stress-strain relation

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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
... strain, plastic strain, and residual stress responses. It also describes the difference between smooth and precracked specimens and how they are used, provides information on slow-strain-rate testing and how to assess the results, and discusses various test environments and procedures, including tests...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040017
EISBN: 978-1-62708-300-3
... Abstract This chapter discusses the role of plastic deformation in forging and the effect of strain and strain rate on metal flow. It demonstrates the use of stress tensors and shows how metal flow can be represented qualitatively by the displacement of volume elements and quantitatively by the...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 2017
DOI: 10.31399/asm.tb.sccmpe2.t55090257
EISBN: 978-1-62708-266-2
... composition, microstructure, and heat treatment. It describes the types of environments where magnesium alloys are most susceptible to SCC and the effect of contributing factors such as temperature, strain rate, and applied and residual stresses. The chapter also discusses crack morphology and what it reveals...
Book Chapter

Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2012
DOI: 10.31399/asm.tb.ffub.t53610025
EISBN: 978-1-62708-303-4
... in pascals  ( Pa )  or pounds per square inch  ( psi ) where P is the load, and A is the instantaneous cross-sectional area. Fig. 11 True stress-true strain behavior. Source: Ref 2 The true stress is related to the engineering stress as follows: (Eq 11) σ...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 February 2005
DOI: 10.31399/asm.tb.chffa.t51040051
EISBN: 978-1-62708-300-3
... velocity field (kinematics as described by velocity, ε and ε ˙ fields). Such a relation exists between the stresses (in principal axes) and strain rates: (Eq 5.11a) ε ˙ 1 = λ ( σ 1 − σ m ) (Eq 5.11b) ε ˙ 2 = λ ( σ 2...
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
... of Goodman, Gerber, and Soderberg relationships. Source: Ref 2 If the design is based on the yield strength, then the yield strength (σ y ) can be used instead of the ultimate strength (σ u ). During cyclic loading within the elastic regime, stress and strain are directly related...
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
... ) ( 2000 ) = 2000 × 10 6  in./in . If a specially orthotropic ply is loaded parallel to the material’s natural axes, the resulting stresses can be related to the accompanying strains by the reduced stiffness [ Q ] matrix: (Eq 16.13)   { σ } = [ Q ] { ɛ...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smff.t53400053
EISBN: 978-1-62708-316-4
... stress state at any point in a material can be expressed in different ways for different purposes. It then compares and contrasts some of the more widely used yield criteria and demonstrates the use of flow rules. It also explains how to calculate power, energy, and effective strain and strain rate and...
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
... with a short crack, the function Y ( a / w ) approaches 1. The function Y ( a / w ) for different geometries and different types of cracks can be found in handbooks on fracture mechanics. The strain energy release rate and stress-intensity approaches are related: (Eq 16) K 2 = E...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540121
EISBN: 978-1-62708-309-6
... applied to cyclic stress-strain and hysteresis data. Damage can be related to results obtained for simple strain-controlled specimens and summed on a cycle-by-cycle basis. A distinct advantage of the strain-life method is its ability to deal with variable-amplitude loading through improved cumulative...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2012
DOI: 10.31399/asm.tb.smfpa.t53500019
EISBN: 978-1-62708-317-1
...), no transverse stresses are developed during bending (σ 2 = σ 3 = 0), and thus, uniaxial deformation conditions exist. Hence, the transverse and longitudinal strains are related (ε 2 = −½ε 1 ), which causes an increase in width in the compression area and a decrease in width in the tension area...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540047
EISBN: 978-1-62708-309-6
... Abstract This chapter examines the phenomena of deformation and fracture in metals, providing readers with an understanding of why it occurs and how it can be prevented. It begins with a detailed review of tension and compression stress-strain curves, explaining how they are produced and what...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 November 2011
DOI: 10.31399/asm.tb.jub.t53290099
EISBN: 978-1-62708-306-5
... progressive steps: recovery, recrystallization, and grain growth. Residual stresses are relieved during recovery, but strength and ductility are largely retained. At higher temperatures, recrystallization occurs through the formation of new strain-free grains, and the strength decreases while the ductility...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2003
DOI: 10.31399/asm.tb.cfap.t69780323
EISBN: 978-1-62708-281-5
.... Source: Ref 31 Critical stresses (or strains) for the crazing of PS, which is internally plasticized with dichlorobenzene to varying degrees, were measured as a function of the T g of the plasticized polymer ( Ref 2 ). It was observed that a similar critical strain dependence on T g is...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 December 2018
DOI: 10.31399/asm.tb.fibtca.t52430343
EISBN: 978-1-62708-253-2
... sufficient to knock out the scale. Slight fluctuation in the steam velocity and turbulence aggravated the scale spallation further. The main cause of exfoliation of the scale formed on the inner surface of the superheater tubes was differential stresses and strains developed on different layers of the...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 January 2015
DOI: 10.31399/asm.tb.spsp2.t54410213
EISBN: 978-1-62708-265-5
... free length at some moment during strain hardening, and ρ is the dislocation density. Equation 11.1 clearly relates increases in flow stress during strain hardening to dynamic dislocation interactions and increases in dislocation density. Figure 11.2 shows changes in dislocation substructure...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 August 2005
DOI: 10.31399/asm.tb.mmfi.t69540169
EISBN: 978-1-62708-309-6
... ). Relating this to the Griffith solution, the strain energy release rate for each crack tip is: (Eq 4.1a) G C = S c 2 π a c /   E for plane stress, and (Eq 4.1b) G IC = S c 2 π a c ( 1 − ν 2 ) / E for plane...
Series: ASM Technical Books
Publisher: ASM International
Published: 01 March 2000
DOI: 10.31399/asm.tb.aet.t68260001
EISBN: 978-1-62708-336-2
... Abstract This chapter discusses the basic differences between direct and indirect extrusion, the application of plastic theory, the significance of strain and strain rate, friction, and pressure, and factors such as alloy flow stress and extrusion ratio, which influence the quality of material...
Series: ASM Technical Books
Publisher: ASM International
Published: 30 April 2021
DOI: 10.31399/asm.tb.tpsfwea.t59300001
EISBN: 978-1-62708-323-2
... mechanics of lubrication. The engineering material community consisted of metallurgists, materials engineers, ceramics engineers, polymer engineers, and mechanical engineers who delved into the stress and strains involved in rubbing contacts. In fact, for the first 40 years of the Wear of Materials...