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R-curve methods

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Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006910
EISBN: 978-1-62708-395-9
... ) for the construction of the crack growth resistance curve ( J-R curve) of polymers. Known as the normalization method, it relies on the representation of J vs Δ a ( Ref 38 – 40 ), trying to overcome some of the problems of the multi-specimen methodology, which are mainly based on uncertainties associated...
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
... is, essentially, a graphical model, shown schematically in Fig. 2 , that reflects the stress-strain curve of the material. The FAD consists of two elements: the failure assessment curve (FAC) and the failure assessment point (FAP). The collapse ratio, S r or L r , is the ratio of the applied stress...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006809
EISBN: 978-1-62708-329-4
... to calculate a toughness ratio, K r , and load ratio, L r , as: (Eq 1) K r = K I P + Φ K I SR K mat (Eq 2) L r = σ ref P σ ys where K I P is the stress-intensity factor based on the primary stress, Φ is the plasticity correction factor, K...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.power.c9001711
EISBN: 978-1-62708-229-7
... + log   t f ) - 7.25 Equation 1 , together with creep rupture stress R m in 100,000 hours, lead to the determination of the specific curve creep stress-rupture strenght vs LMP for each steel. Thus, Table 1 shows the values of R m for the three steels considered, 10CrMo9-10...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006930
EISBN: 978-1-62708-395-9
... 1) σ ( R ) c o r r = σ ( R ) a p p ( 3 + d log ( σ a p p ) / d log ( γ ̇ ) ) / 4 In the case of melt rheology, there are limits to the slope of the log ( σ app ) versus log (γ̇) curve. In the Newtonian limit, the slope...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
... σ = σ max − σ min Stress amplitude: σ a = Δ σ 2 Mean stress: σ m = σ max + σ min 2 Stress ratio: R = σ min σ max Amplitude ratio: A = σ a σ m Fig. 2 Basic definitions of a cycle...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003516
EISBN: 978-1-62708-180-1
...-compression loading cycle. For an R -ratio of −1, the loading is fully reversed and the mean stress is consequently 0. The results of fatigue tests run at R = −1 are plotted on an S - N curve, as shown in Fig. 2 , to establish an endurance limit for the material. For low-strength steels, the endurance...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006928
EISBN: 978-1-62708-395-9
... versus strain, r , during the test; the slope of the curve obtained is the flexural modulus. Flexural moduli for various plastics are compared in Fig. 12 . Fig. 12 Flexural modulus of engineering plastics at elevated temperatures. PET, polyethylene terephthalate; PBT, polybutylene terephthalate...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006929
EISBN: 978-1-62708-395-9
..., κ is the rate of saturation defined as π 2 D γ / ( 2 δ ) 2 where δ is the specimen thickness, t is the exposure time, and r l ± is a variable defined as [ ( κ l 2 + γ + β ) ± ( κ l 2 + γ + β ) 2 − 4...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006934
EISBN: 978-1-62708-395-9
... y RT ) where ε ̇ 0 is a constant preexponential strain rate, Δ H a is the activation enthalpy, R is the universal gas constant, and v a is the activation volume for shear flow under a shear stress,σ y . Criteria for Shear Yielding Stress-strain curves of polymers...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003517
EISBN: 978-1-62708-180-1
... Abstract This article focuses on the life assessment methods for elevated-temperature failure mechanisms and metallurgical instabilities that reduce life or cause loss of function or operating time of high-temperature components, namely, gas turbine blade, and power plant piping and tubing...
Series: ASM Handbook
Volume: 11B
Publisher: ASM International
Published: 15 May 2022
DOI: 10.31399/asm.hb.v11B.a0006937
EISBN: 978-1-62708-395-9
... Reflection loss is calculated as a close approximation by the formula: R = ( n 1 − n ) 2 ( n 1 + n ) 2 where n and n 1 are the indexes of refraction of the two media involved ( Ref 1 ). If a material has a refractive index of 1.49 (at 589 nm), such as acrylic, and the second...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003528
EISBN: 978-1-62708-180-1
... roughness on the same specimen. The stress was then measured in the three regions via XRD techniques under independently monitored tensile loads. X-ray diffraction results were plotted versus the applied stress for locations where the average roughness ( R a ) was 1, 3, and 6 μm (1 μm = 39.4 μin...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006768
EISBN: 978-1-62708-295-2
... results were plotted versus the applied stress for locations where the average roughness ( R a ) was 1, 3, and 6 μm (1 μm = 39.4 μin.). The linear least squares regression for each data set yielded slopes of 1.01, 0.96, and 1.03 for 1, 3, and 6 μm R a , respectively ( Fig. 6a ). All of these results...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006779
EISBN: 978-1-62708-295-2
... m ) Safe-life, finite-life Local strain concept Low-cycle fatigue curve, ε a = f ( N i ) Cyclic stress-strain (σ a -ε a ) curve Damage tolerance Fracture mechanics concept Threshold value, Δ K th Crack growth diagram, da / dN = f (Δ K , R ) Fracture toughness, K Ic...
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
... 2   It was noted that Eq 15 is the equation of a circle with axes σ and τ and centered on the σ-axis with: (Eq 16) Center = ( σ x   +   σ y 2 ) and radius, R , given by: (Eq 17) R 2 = (   σ x   +   σ y 2 ) 2 +   τ...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003536
EISBN: 978-1-62708-180-1
... roughness parameter on the ruler length η. (b) Plot of R L (η) versus η for fracture profile from the tensile fracture surface of AISI 4340 steel. Source: Ref 4 Another popular method for measurement of fractal dimension is the slit-island method proposed by Mandelbrot ( Ref 8 ). In this method...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.bldgs.c9001715
EISBN: 978-1-62708-219-8
..., thermal or residual nature can be included in the analysis and the analysis can allow for flaw growth. To use the method, two parameters, S r and K r are calculated and plotted on a failure assessment diagram. The stress term, S r , evaluates criticality of a structural member against plastic collapse...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.power.c9001004
EISBN: 978-1-62708-229-7
... which ranged between −0.74 to −1.85µamps averaging −1.35µamps while the de-embrittled material showed I r data between −0.89 to −2.36µamps averaging −.173µamps. A typical EPR test curve is shown in Figure 10 while the scatter and overalpping nature of the embrittled and de-embrittled material EPR...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006801
EISBN: 978-1-62708-329-4
..., but experimental data ( Ref 2 ) suggest designing with a tooling radius at least four times the metal thickness ( r / t > 4). There probably is some variation based on grade, strength level, and microstructure. Fig. 3 Shear fracture occurring on radius ( r ). Courtesy of J. Dykeman, Honda Wrinkles...