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elastic-plastic stress integration

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Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003513
EISBN: 978-1-62708-180-1
... assessment point; J e , elastic component of J -integral; J p , plastic component of J -integral; δ e , elastic component of crack-tip opening displacement; δ p , plastic component of crack-tip opening displacement; K I , mode I stress-intensity factor; K mat , general linear elastic fracture...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003305
EISBN: 978-1-62708-176-4
... in limiting of operating stresses. It describes the mechanisms, testing methods, and effecting parameters of two main categories of fracture mechanics: linear-elastic fracture mechanics and elastic-plastic fracture mechanics. The article concludes with a discussion on the three major progressive stages...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.9781627081931
EISBN: 978-1-62708-193-1
Series: ASM Handbook
Volume: 14B
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v14b.a0005131
EISBN: 978-1-62708-186-3
.... This approximation, adopted for simplicity, has little effect on the result. The moment consists of three terms, the first two identical to the elastic, perfectly plastic result, that is, Eq 12 (with yield stress, σ 0 ), and the third an integral corresponding to the additional moment caused by the hardening...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002383
EISBN: 978-1-62708-193-1
... Failure stress (test), MPa 200 160 190 β 1,017 1,017 1.19 H (rough approximation) 32 10 2000 Toughness, K c , Eq 15 , MPa m 2550 2039 … J elastic , Eq 14 , N/mm 94.2 20.1 … J plastic , Eq 17 , N/mm 0.3 (a) 67.1 … J total = dW / da , Eq 19 , N...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002470
EISBN: 978-1-62708-194-8
... -integral ( Ref 5 , 16 , 17 ). Further discussion on the J -integral and elastic-plastic fracture mechanics is presented in the next section of this article. Categories of Fracture Mechanics Fracture mechanics is a broad subject, but there are fundamentally two categories: linear elastic fracture...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005424
EISBN: 978-1-62708-196-2
... that its integral over the fundamental region is unity. Kinematic Framework for Deforming Crystals and Polycrystals The two modes of straining, elastic and plastic, jointly must produce a single compatible deformation. As depicted in Fig. 3 , this is accomplished by a multiplicative decomposition...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003310
EISBN: 978-1-62708-176-4
... originally developed to characterize the elastic-plastic fracture of ductile metallic materials are most commonly used (with slight modifications) to characterize ductile polymers. These methods are based on the concept of the J -integral to determine plane strain fracture toughness values. To date...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003546
EISBN: 978-1-62708-180-1
.... The peak elastic stress in Fig. 8 is consistently above the yield strength of the 2.25Cr-1Mo steel at the operating temperatures and the elastic stress range exceeds twice the cyclic yield strength. Therefore, the material in the vicinity of the steam passageway bores undergoes plastic deformation during...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002386
EISBN: 978-1-62708-193-1
... conditions of plastic collapse and linear (elastic) fracture mechanics. The CEGB R6 method ( Ref 1 ) uses a failure assessment diagram ( Fig. 10 ), which plots the ratio K r = K / K c versus the ratio S r = σ/σ fc (where σ fc is the stress for plastic collapse). This normalization makes...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002378
EISBN: 978-1-62708-193-1
... configurations. More recent advancements in the state of the art, such as R -curve and J -integral tests, have extended the use of fracture mechanics to elastic-plastic conditions which are associated with lower-strength materials and smaller section sizes. However, when stresses approach or exceed yield...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.9781627081764
EISBN: 978-1-62708-176-4
Series: ASM Handbook
Volume: 1A
Publisher: ASM International
Published: 31 August 2017
DOI: 10.31399/asm.hb.v01a.a0006307
EISBN: 978-1-62708-179-5
... is referred to as the ultimate tensile strength, and often the Greek letters σ and ε are used for stress and strain, respectively. The shape of the stress-strain curve consists of at least two different major phenomena: Elastic deformation, which is reversible Plastic deformation, which...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.9781627081801
EISBN: 978-1-62708-180-1
Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003224
EISBN: 978-1-62708-199-3
... for linear-elastic displacement during slow testing of certain specimen configurations. Advancements in the state of the art, such as R -curve and J -integral tests, extend the use of fracture mechanics to elastic-plastic conditions, which are associated with lower strength materials and smaller section...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003399
EISBN: 978-1-62708-195-5
... and stress distribution under linear elastic conditions Stress-strain response and stress distribution under elastic-plastic or elastic-viscoplastic conditions It should be pointed out, especially to those familiar with PMCs, that while MMCs are often fabricated from lamina, the processing...
Series: ASM Handbook
Volume: 22B
Publisher: ASM International
Published: 01 November 2010
DOI: 10.31399/asm.hb.v22b.a0005506
EISBN: 978-1-62708-197-9
... residual stress and strain distributions that remain in the beam after being subject to plastic deformation during the loading, followed by the elastic unloading. The resulting distributions exhibit some interesting characteristics. Inside the elastic region ( y < ±40 mm), where stress and strain...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005431
EISBN: 978-1-62708-196-2
... of a constitutive equation is the well-known Hooke's law in the elastic regime: (Eq 3) σ = ε E where E is the elastic modulus of the material, which is measured in a simple tension test or by ultrasonic means. During plastic deformation of most metallic materials, the stress-strain curve becomes...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002469
EISBN: 978-1-62708-194-8
... and shutdown operations. The elastically stressed neighborhood limited the strains of the inelastic deformation region associated with stress riser. The plastic zone is considered to be under strain control by the surrounding elastic material. In testing, strain control eliminates potentially large strains...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... elastic.) Above the yield stress, material behavior is nonlinear, and plastic strain results from increased stress. The volume of the material is assumed to be constant, and Eq 34 shows that ν approaches 0.5 for a constant-volume material. The relationship between stress and strain in the plasticity...