Analysis of Plastic Zone at a Crack Tip for I, II and III Mode Fracture with MY Criterion

2014 ◽  
Vol 1078 ◽  
pp. 25-30
Author(s):  
Miao Guan ◽  
Zhao Zhun Zhong
Keyword(s):  
Plastic Zone ◽  
Yield Stress ◽  
Yield Criterion ◽  
Polar Angle ◽  
Small Scale ◽  
Strength Factor ◽  
Plastic Zones ◽  
Tresca Criterion ◽  
Plain Strain ◽  
My Criterion

The plastic zones for I, II, III mode crack under small scale yielding are analyzed by MY criterion, and the analytical solutions of the sizes of the plastic zones for plain stress and plain strain states are first obtained. The solutions for I and II mode crack show that the two solutions are functions of the yield stress, stress strength factor and polar angle, while the solution for III mode crack just depends on the yield stress and stress strength factor. Comparison of the plastic zone with those based on Tresca and Mises criteria shows that Tresca criterion predicts the maximum, the result by MY yield criterion lies between them, and is very close to that by Mises criterion. Besides, the relationship of plastic zone between plain stress and plain strain are also discussed.

Application of GM Yield Criterion in Plastic Zone of ModeⅠCrack and Burst Pressure for Pipeline

2011 ◽  
Vol 399-401 ◽  
pp. 2189-2194 ◽  
Author(s):  
De Wen Zhao ◽  
Can Ming Li ◽  
Liang Yun Lan ◽  
Shun Hu Zhang
Keyword(s):  
Plastic Zone ◽  
Pipeline Steel ◽  
Yield Criterion ◽  
Burst Pressure ◽  
Mode I ◽  
Strain Condition ◽  
Stress Criterion ◽  
Tresca Criterion ◽  
Plain Strain ◽  
Gm Yield Criterion

Based on GM yield criterion, the analytical solutions for shape and size of mode I crack tip plastic zone and the burst pressure for X70 pipeline steel are derived. Comparing the solutions with those based on Mises and Trasca criteria shows that under plain strain condition the area of plastic zone on GM is between Tresca and Mises solutions, and very close to Mises one. Among the areas Tresca’s is the largest and Mises is the smallest and all three zones are dumbbell shaped. However, for pipeline burst pressure based on Tresca criterion is the smallest and that on Twin shear stress criterion (TSS) is the largest, those on GM and Mises are also very close to each other and lie between Tresca and TSS results.

A Plastic Zone Equation Based on Mean Yield Criterion

2010 ◽  
Vol 97-101 ◽  
pp. 534-537 ◽  
Author(s):  
Wei Deng ◽  
De Wen Zhao ◽  
Xiao Mei Qin ◽  
Xiu Hua Gao ◽  
Chun Lin Qiu ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Analytical Solution ◽  
Plastic Zone ◽  
Yield Criterion ◽  
Small Scale ◽  
Mode I ◽  
Mode I Crack ◽  
Small Scale Yielding ◽  
Scale Yielding ◽  
My Criterion

Based on mean yield criterion, an analytical solution for the mode I crack tip plastic zone (CTPZ) under small scale yielding was derived. The results reveal that the size of CTPZ determined by MY criterion is between those by Mises’ yield criterion the smallest, and by Tresca’s criterion the largest; while the zone is almost coincide with that by Mises’ one. The size of CTPZ is related to the ratio of fracture toughness to yield strength; with increasing of the ratio, the size of the zone increases, meaning the better of fracture toughness.

On Elastic-Plastic Fracture Behavior of a Half-Space Under Prescribed Loading

2017 ◽  
Vol 09 (03) ◽  
pp. 1750036 ◽  
Author(s):  
Jing Yang ◽  
Kun Zhou
Keyword(s):  
Plastic Zone ◽  
Half Space ◽  
Plastic Zone Size ◽  
Small Scale ◽  
Dugdale Model ◽  
Perfectly Plastic ◽  
Crack Tips ◽  
Scale Yielding ◽  
Plastic Zones ◽  
Elastic Perfectly Plastic

The plastic zones at crack tips play a significant role in fracture behaviors of materials. In this paper, a semi-analytic solution is proposed for the plastic zone size of cracks in an elastic-perfectly plastic half-space under prescribed loading. This solution also considers the subsurface stress distribution influenced by the plastic zones at crack tips. The cracks can be treated as a distribution of edge dislocations with unknown densities by using the distributed dislocation technique. In order to calculate the plastic zone sizes of crack tips, two stripes ahead of crack tips are introduced as plastic zones based on the Dugdale model of small scale yielding. The numerical values can be determined by canceling the stress intensity factor due to the closure stress and that due to the applied load. It is noted that the plastic zone sizes are affected by the crack length and depth, yield strength of substrates and loading conditions.

Limit Analysis of Defect-Free Pipe Elbow under Internal Pressure with MY Criterion

2011 ◽  
Vol 127 ◽  
pp. 79-84 ◽  
Author(s):  
Shun Hu Zhang ◽  
De Wen Zhao ◽  
Cai Ru Gao
Keyword(s):  
Yield Criterion ◽  
Limit Load ◽  
Burst Pressure ◽  
Curvature Radius ◽  
Average Radius ◽  
Straight Pipe ◽  
Pipe Elbow ◽  
Inner Pressure ◽  
Tresca Criterion ◽  
My Criterion

With MY (mean yield) criterion, the limit load of defect-free pipe elbow under inner pressure is analyzed, and an analytical solution is first obtained. The solution shows that the limit load is a function of wall thicknesst, average radiusr, yield strength as well as curvature radiusR0. The limit load increases with the increase of the curvature radiusR0and will get the same value with the burst pressure of straight pipe ifR0→∞. The limit load calculated by the solution is compared with those based on Tresca, Mises, as well as TSS yield criteria. It is also concluded that Tresca criterion predicts a lower bound to the limit load, while TSS criterion predicts an upper bound one. However, the limit load based on the MY criterion lies just between the TSS and Tresca solutions, most notably, the MY criterion almost has the same prediction precision with Mises solution.

Plastic Strain Distribution at the Tips of Propagating Fatigue Cracks

1976 ◽  
Vol 98 (1) ◽  
pp. 24-29 ◽  
Author(s):  
D. L. Davidson ◽  
J. Lankford
Keyword(s):  
Aluminum Alloy ◽  
Fatigue Crack ◽  
Plastic Strain ◽  
Plastic Zone ◽  
Strain Distribution ◽  
Dimensionless Parameter ◽  
Fatigue Cracks ◽  
Crack Tip ◽  
Cyclic Plastic Zone ◽  
Plastic Zones

The techniques of selected area electron channeling and positive replica examination have been used to study the plastic zones attending fatigue crack propagation in 304 SS, 6061-T6 aluminum alloy, and Fe-3Si steel. These observations allowed the strain distribution at the crack tip to be determined. The results indicate that the concepts of a monotonic and a cyclic plastic zone are essentially correct, with the strains at demarcation between these two zones being 3 to 6 percent. Strain distribution varies as r−1/2 in the cyclic zone and as ln r in the monotonic plastic zone. The strain distributions for all materials studied may be made approximately coincident by using a dimensionless parameter related to distance from the crack tip.

X-Ray Fractography Evaluation of the Plastic Zones of Dynamic Fracture

1992 ◽  
Vol 36 ◽  
pp. 551-560
Author(s):  
Kazuyuki Matsui ◽  
Osamu Nakada ◽  
Yukio Hirose ◽  
Keisuke Tanaka
Keyword(s):  
Stress Intensity Factor ◽  
Plastic Zone ◽  
Dynamic Fracture ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Plastic Zone Size ◽  
Zone Size ◽  
X Ray Diffraction ◽  
X Ray ◽  
Plastic Zones

AbstractTo evaluate the plastic zones of dynamic fracture, instrumented Charpy impact tests of high carbon bearing steels are conducted. The amount of plastic zone size left on the fracture surface is evaluated from the X-ray diffraction profiles. An analysis is presented of the relationship between the X-ray diffraction profiles and fracture mechanics parameters. The results are discussed in correlations between dynamic stress intensity factor and absorbed energy values. A good correlation exists between the plastic zone size and the dynamic stress intensity factor.The fraction of retained austenite is determined from X-ray diffraction profiles at surfaces of fractures and also beneath the surfaces of fractures.It shows the work hardening is introduced by the strain energy in the plastic zones. The values of the proportionality constant, α, determined for various kinds of dynamic fracture are related to half-value breadth by the functionwhere B0 and BF are average of half-value breadth which are given by core of material and plastic zone of dynamic fracture.

scholarly journals Low-temperature rheology of calcite

2019 ◽  
Vol 221 (1) ◽  
pp. 129-141 ◽  
Author(s):  
Michael K Sly ◽  
Arashdeep S Thind ◽  
Rohan Mishra ◽  
Katharine M Flores ◽  
Philip Skemer
Keyword(s):  
Low Temperature ◽  
Yield Stress ◽  
Low Temperatures ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Polycrystalline Sample ◽  
Small Scale ◽  
Indentation Hardness ◽  
Micropillar Compression ◽  
Flow Laws

SUMMARY Low-temperature plastic rheology of calcite plays a significant role in the dynamics of Earth's crust. However, it is technically challenging to study plastic rheology at low temperatures because of the high confining pressures required to inhibit fracturing. Micromechanical tests, such as nanoindentation and micropillar compression, can provide insight into plastic rheology under these conditions because, due to the small scale, plastic deformation can be achieved at low temperatures without the need for secondary confinement. In this study, nanoindentation and micropillar compression experiments were performed on oriented grains within a polycrystalline sample of Carrara marble at temperatures ranging from 23 to 175 °C, using a nanoindenter. Indentation hardness is acquired directly from nanoindentation experiments. These data are then used to calculate yield stress as a function of temperature using numerical approaches that model the stress state under the indenter. Indentation data are complemented by uniaxial micropillar compression experiments. Cylindrical micropillars ∼1 and ∼3 μm in diameter were fabricated using a focused ion beam-based micromachining technique. Yield stress in micropillar experiments is determined directly from the applied load and micropillar dimensions. Mechanical data are fit to constitutive flow laws for low-temperature plasticity and compared to extrapolations of similar flow laws from high-temperature experiments. This study also considered the effects of crystallographic orientation on yield stress in calcite. Although there is a clear orientation dependence to plastic yielding, this effect is relatively small in comparison to the influence of temperature.

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