scholarly journals The effect of a crack-tip radius on the validity of the singular solution

2004 ◽  
Vol 218 (7) ◽  
pp. 693-701 ◽  
Author(s):  
D Dini ◽  
D A Hills
Keyword(s):  
Singular Solution ◽  
Edge Crack ◽  
Process Zone ◽  
Crack Tip ◽  
Local Stress ◽  
Scaling Factor ◽  
Root Radius ◽  
Finite Crack ◽  
Tip Radius ◽  
Local Stress Field

The influence of the finite crack-root radius on the local stress field at the root of a crack is found explicitly. This is then applied as an inner asymptotic solution, embedded with the conventional crack-tip singular solution, to quantify the possible influence of local rounding on the ability of the singular solution to capture the characteristics of the crack-tip process zone. The scaling factor employed is the conventional crack-tip stress intensity, and the example of a simple edge crack in a tension field is used to illustrate the method.

Simulation of anisotropic crack tip deformation processes and particle interactions in toughened polymers

2019 ◽  
Vol 28 (1) ◽  
pp. 3-13
Author(s):  
Garrett Nygren ◽  
Ryan L Karkkainen
Keyword(s):  
Polymer Chain ◽  
Process Zone ◽  
Crack Tip ◽  
Local Stress ◽  
Material Design ◽  
Initial Study ◽  
Yield Zone ◽  
Particle Spacing ◽  
Deformation Processes ◽  
Local Yielding

This study develops a finite element-based simulation of submicrometer crack tip deformation processes in polymers to investigate local toughening effects. An initial study of how these processes interact with stiff inclusions is presented to enable further investigation of particulate toughening. Crack tip and process zone mechanisms, including polymer chain disentanglement, directional chain realignment with consequent anisotropy, and crack propagation, are considered in a dedicated user-defined material law. Such processes are generally homogenized on higher scale continuum levels analyses, but direct simulation can provide insight into toughening mechanisms that have been widely observed but not fully explained. The user material law herein was employed in a parametric study to investigate the relative importance of (1) the extent of local inelastic polymer chain realignment and (2) consequent anisotropic hardening of the realigned polymer chains. In order to explore the interaction of fracture processes with nanometer-scale inclusions, silica particles with varied spacing were also included in the simulations. The interaction between local stress concentration and energy dissipation mechanisms has been quantified. It is shown that in neat polymers, local yielding is the dominant toughening effect accounting for over 90% of the local energy absorption, whereas local stiffening alone would decrease toughness. Stiff inclusions were shown to generally decrease toughness, except in cases where local yielding greatly outweighs local stiffening effects. Roughly 45% increase in toughness was shown for a 250-nm particle spacing that balances the acceleration of elastic failure with the formation of a larger local yield zone size. This demonstrates the utility of employing dedicated material laws to microstructural scale analyses in providing design targets in material design.

Effect of Carbon Black on the J-Integral and Strain Energy in the Crack Tip Region in a Vulcanized Natural Rubber

1987 ◽  
Vol 60 (5) ◽  
pp. 893-909 ◽  
Author(s):  
H. Liu ◽  
R. F. Lee ◽  
J. A. Donovan
Keyword(s):  
Energy Density ◽  
Carbon Black ◽  
Strain Energy ◽  
Process Zone ◽  
Crack Tip ◽  
Local Strain ◽  
Biaxial Stress ◽  
J Integral ◽  
Tearing Energy ◽  
Tip Radius

Abstract 1) The J-integral is path independent in both PS and SEN specimens and equals the tearing energy. 2) The critical J-integral at initiation is less in PS specimens than in SEN specimens, because the greater biaxial stress in PS restricts the process zone. 3) At initiation, the crack-tip radius, proportional to the local strain, is independent of CB. 4) The energy density within and the size of the process zone near the crack tip increase with CB; these are major contributions to CB reinforcement.

Lifetime Prediction of Components Including Initiation Phase

2006 ◽  
Author(s):  
Michael Besel ◽  
Angelika Brueckner-Foit
Keyword(s):  
Input Data ◽  
Local Stress ◽  
Fatigue Loading ◽  
Computer Code ◽  
Lifetime Distribution ◽  
Element Analysis ◽  
Initiation Phase ◽  
Mechanics Model ◽  
Critical Regions ◽  
Local Stress Field

The lifetime distribution of a component subjected to fatigue loading is calculated using a micro-mechanics model for crack initiation and a fracture mechanics model for crack growth. These models are implemented in a computer code which uses the local stress field obtained in a Finite Element analysis as input data. Elemental failure probabilities are defined which allow to identify critical regions and are independent of mesh refinement. An example is given to illustrate the capabilities of the code. Special emphasis is put on the effect of the initiation phase on the lifetime distribution.

Comparison of Strip Yield and Net Section Plasticity Models for a Bar in Bending With a Single Edge Crack

2017 ◽  
Author(s):  
Wolf Reinhardt ◽  
Don Metzger
Keyword(s):  
Edge Crack ◽  
Large Scale ◽  
Stress Singularity ◽  
Crack Tip ◽  
Small Scale ◽  
Single Edge ◽  
Yield Model ◽  
Strip Yield Model ◽  
Crack Tip Plasticity ◽  
Stress And Deformation

The strip yield model is widely used to describe crack tip plasticity in front of a crack. In the strip yield model the stress in the plastic zone is considered as known, and stress and deformation fields can be obtained from elastic solutions using the condition that the crack tip stress singularity vanishes. The strip yield model is generally regarded to be valid to describe small scale plasticity at a crack tip. The present paper examines the behavior of the strip yield model at the transition to large-scale plasticity and its relationship to net section plasticity descriptions. A bar in bending with a single edge crack is used as an illustrative example to derive solutions and compare with one-sided and two-sided plasticity solutions.

scholarly journals Crack Tip Radius Effect on Fatigue Crack Growth and Near Tip Fields in Plastically Compressible Materials

2021 ◽  
Vol 71 (2) ◽  
pp. 248-255
Author(s):  
S. Singh ◽  
D. Khan
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Crack Growth ◽  
Strain Softening ◽  
Crack Tip ◽  
Initial Crack ◽  
Strain Fields ◽  
Tip Radius ◽  
Compressible Materials ◽  
Structural Polymers

Motivated by the prospective uses of plastically compressible materials such as, metallic and polymeric foams, transformation toughened ceramics, toughened structural polymers etc., the present authors investigate the crack-tip radius effect on fatigue crack growth (FCG) of a mode I crack and near-tip stress-strain fields in such plastically compressible solids. These plastically compressible materials have been characterised by elastic-viscoplastic constitutive equations. Simulations are conducted for plane strain geometry with two different hardness functions: one is bilinear hardening and the other one is hardening-softening-hardening. It has been observed that plastic compressibility as well as strain softening lead to significant deviation in the amount of crack growth. It has further been revealed that the nature of FCG is appreciably affected by initial crack-tip radius. Even though it may look from outside that the increase in tip radius will lead to decrease in FCG, but the nature of FCG variation with respect to tip radius is found to be a combined effect of tip radius, plastic compressibility and work or strain softening etc.

scholarly journals Activation of optimally and unfavourably oriented faults in a uniform local stress field during the 2011 Prague, Oklahoma, sequence

2020 ◽  
Vol 222 (1) ◽  
pp. 153-168 ◽  
Author(s):  
Elizabeth S Cochran ◽  
Robert J Skoumal ◽  
Devin McPhillips ◽  
Zachary E Ross ◽  
Katie M Keranen
Keyword(s):  
Stress Field ◽  
Compressive Stress ◽  
Local Stress ◽  
Wastewater Disposal ◽  
Principal Compressive Stress ◽  
Vertical Fault ◽  
Major Fault ◽  
Pressure Changes ◽  
Earthquake Sequences ◽  
Local Stress Field

SUMMARY The orientations of faults activated relative to the local principal stress directions can provide insights into the role of pore pressure changes in induced earthquake sequences. Here, we examine the 2011 M 5.7 Prague earthquake sequence that was induced by nearby wastewater disposal. We estimate the local principal compressive stress direction near the rupture as inferred from shear wave splitting measurements at spatial resolutions as small as 750 m. We find that the dominant azimuth observed is parallel to previous estimates of the regional compressive stress with some secondary azimuths oriented subparallel to the strike of the major fault structures. From an extended catalogue, we map ten distinct fault segments activated during the sequence that exhibit a wide array of orientations. We assess whether the five near-vertical fault planes are optimally oriented to fail in the determined stress field. We find that only two of the fault planes, including the M   5.7 main shock fault, are optimally oriented. Both the M 4.8 foreshock and M   4.8 aftershock occur on fault planes that deviate 20–29° from the optimal orientation for slip. Our results confirm that induced event sequences can occur on faults not optimally oriented for failure in the local stress field. The results suggest elevated pore fluid pressures likely induced failure along several of the faults activated in the 2011 Prague sequence.

Investigation of Constraint Effects on Fracture Toughness for CC(T) Specimens

2004 ◽  
Author(s):  
Dieter Siegele ◽  
Igor Varfolomeyev ◽  
Kim Wallin ◽  
Gerhard Nagel
Keyword(s):  
Fracture Toughness ◽  
Crack Tip ◽  
Temperature Shift ◽  
Local Stress ◽  
Significant Loss ◽  
Reference Temperature ◽  
T Stress ◽  
Local Stress State ◽  
Constraint Effects ◽  
Crack Tip Constraint

Within the framework of the European research project VOCALIST, centre cracked tension, CC(T), specimens made of an RPV steel were tested and analysed to quantify the influence of local stress state on fracture toughness. The CC(T) specimens demonstrate a significant loss of crack tip constraint resulting in a considerable increase in fracture toughness as compared to standard fracture mechanics specimens. So, the master curve reference temperature, To, determined on the basis of CC(T) tests performed in this study is about 43°C lower than To obtained on standard C(T) specimens. Finite element analyses of the tests revealed that the above experimental finding is in a good agreement with the empirical correlations between the reference temperature shift and the crack tip constraint as characterised by the T-stress or Q parameter (Wallin, 2001; Wallin, 2004). The results of this work are consistent with a number of other tests performed within the VOCALIST project and contribute to the validation of engineering methods for the crack assessment in components taking account of constraint.

Sign in / Sign up

Export Citation Format

Share Document