Adjusted J-R Toughness Curve for Pipes Using J-A2 Crack Constraint of CT Specimens and 3D Crack Meshes

2019 ◽  
Author(s):  
Greg Thorwald ◽  
Ken Bagnoli
Keyword(s):  
Fracture Mechanics ◽  
Test Data ◽  
Crack Front ◽  
Test Specimen ◽  
Closed Form Solution ◽  
Form Solution ◽  
Specimen Geometry ◽  
Ductile Tearing ◽  
Two Parameter ◽  
Axial Surface

Abstract The objective of this paper is to use two-parameter fracture mechanics to adjust a material J-R resistance curve (i.e. toughness) from the test specimen geometry to the cracked component geometry. As most plant equipment is designed and operated on the “upper shelf”, a ductile tearing analysis may give a more realistic assessment of flaw tolerance. In most cases, tearing curves are derived from specimen geometries that ensure a high degree of constraint, e.g., SENB and CT Therefore, there can be significant benefit in accounting for constraint differences between the specimen geometry and the component geometry. In one-parameter fracture mechanics a single parameter, K or J-integral, is sufficient to characterize the crack front stresses. When geometry dependent effects are observed, two-parameter fracture mechanics can be used to improve the characterization of the crack front stress, using T-stress, Q, or A2 constraint parameter. The A2 parameter was be used in this study. The usual J-R power-law equation has two coefficients to curve-fit the material data (ASTM E1820). The adjusted J-R curve coefficients are modified to be a function of the A2 constraint parameter. The measured J-R values and computed A2 constraint values are related by plotting the J-R test data versus the A2 values. The A2 constraint values are computed by comparing the HRR stress solution to the crack front stress results of the test specimen geometry using elastic-plastic FEA. Solving for the two J-R curve coefficients uses J values at two Δa crack extension values from the test data. A closed-form solution for the adjusted J-R coefficients uses the properties of natural logarithms. The solution shows the adjusted J-R exponent coefficient will be a constant value for a particular material and test specimen geometry, which simplifies the application of the adjusted J-R curve. A different test specimen geometry can be used to validate the adjusted J-R curve. Choosing another test specimen geometry, having a different A2 constraint value, can be used to obtain the adjusted J-R curve and compare it to the measured J-R curves. The geometry of the component is also expected to have a different A2 constraint compared to the material test specimen. The example examined here is an axial surface flaw in a pipe. The A2 constraint for an axial surface cracked pipe is computed and used to obtain an adjusted J-R curve. The adjusted J-R curve shows an increase in toughness for the pipe as compared to the CT measured value. The adjusted J-R curve can be used to assess flaw stability using the driving force method or a ductile tearing instability analysis.

scholarly journals Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

2002 ◽  
Author(s):  
P.-S. Lam ◽  
Y. J. Chao ◽  
X.-K. Zhu ◽  
Y. Kim ◽  
R. L. Sindelar
Keyword(s):  
Carbon Steel ◽  
Test Data ◽  
Storage Tank ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Form Solution ◽  
Fracture Parameter ◽  
Element Analysis ◽  
Crack Tip Constraint ◽  
Senb Specimen

Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A two-parameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A2, while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-R curves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and reasonable agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

scholarly journals Determination of Constraint-Modified J-R Curves for Carbon Steel Storage Tanks

2003 ◽  
Vol 125 (2) ◽  
pp. 136-143 ◽  
Author(s):  
P.-S. Lam ◽  
Y. J. Chao ◽  
X.-K. Zhu ◽  
Y. Kim ◽  
R. L. Sindelar
Keyword(s):  
Carbon Steel ◽  
Test Data ◽  
Storage Tank ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Form Solution ◽  
Fracture Parameter ◽  
Element Analysis ◽  
Crack Tip Constraint ◽  
Senb Specimen

Mechanical testing of A285 carbon steel, a storage tank material, was performed to develop fracture properties based on the constraint theory of fracture mechanics. A series of single edge-notched bend (SENB) specimen designs with various levels of crack tip constraint were used. The variation of crack tip constraint was achieved by changing the ratio of the initial crack length to the specimen depth. The test data show that the J-R curves are specimen-design-dependent, which is known as the constraint effect. A two-parameter fracture methodology is adopted to construct a constraint-modified J-R curve, which is a function of the constraint parameter, A2, while J remains the loading parameter. This additional fracture parameter is derived from a closed form solution and can be extracted from the finite element analysis for a specific crack configuration. Using this set of SENB test data, a mathematical expression representing a family of the J-R curves for A285 carbon steel can be developed. It is shown that the predicted J-Rcurves match well with the SENB data over an extensive amount of crack growth. In addition, this expression is used to predict the J-R curve of a compact tension specimen (CT), and reasonable agreement to the actual test data is achieved. To demonstrate its application in a flaw stability evaluation, the configuration of a generic A285 storage tank with a postulated axial flaw is used. For a flaw length of 10% of the tank height, the predicted J-R curve is found to be similar to that for a SENB specimen with a short notch, which is in a state of low constraint. This implies that the use of a J-R curve from the ASTM (American Society for Testing and Materials) standard designs, which typically are high-constraint specimens, may be overly conservative for analysis of fracture resistance of large structures.

A Generalized Impact-Sliding Fretting Wear Model Based on Fracture Mechanics Approach

2004 ◽  
Author(s):  
Yemane Gessesse ◽  
Helmi Attia ◽  
M. O. M. Osman
Keyword(s):  
Fracture Mechanics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fretting Wear ◽  
Simultaneous Action ◽  
Wear Process ◽  
Inconel 600 ◽  
Order Of Magnitude ◽  
Flow Induced Vibrations ◽  
Physical Attributes

Impact-sliding fretting wear is a complex phenomenon due to the random nature of the flow-induced vibrations, and the self-induced tribological changes. Available models, which relate wear losses to the process variables, are empirical in nature and bear no physical similarity to the actual mathematical and physical attributes of the wear process. A generalized model is developed in the present work to mathematically describe the fretting wear process under various modes of motion, namely, impact, sliding and oscillatory. This model, which is based on the findings from the fracture mechanics analysis of the crack initiation and propagation processes, takes into consideration the simultaneous action of both the surface adhesion and subsurface fatigue mechanisms. The model also accounts for the micro-, and macro- contact configuration of the tube-support system. The closed form solution requires the calibration of single parameter, using a limited number of experiments, to account for the effect of environment and the support material. The model was validated using experimental data that are generated for Inconel 600 and Incology 800 tube materials at room and high temperature environment, and for different types of motion. The results showed that model can accurately predict wear losses within a factor of < ±3. This narrow range presents better than an order of magnitude improvement over the current state-of-the-art models.

Two-Parameter Elastic-Plastic Fracture Mechanics Analysis of Surface Cracked Plates Under Uniaxial and Biaxial Loading

2011 ◽  
Author(s):  
Xin Wang
Keyword(s):  
Fracture Mechanics ◽  
Cleavage Fracture ◽  
Crack Front ◽  
Biaxial Loading ◽  
Small Scale ◽  
Elastic Plastic ◽  
Cracked Plates ◽  
Scale Yielding ◽  
Two Parameter ◽  
Uniaxial And Biaxial Loading

In this paper, the J-Q two-parameter elastic-plastic fracture mechanics approach is used to analyse the surface cracked plates under uniaxial and biaxial loading. First, the J-Q characterization of crack front stress fields of surface cracked plates under uniaxial and biaxial tension loadings are discussed. The complete J-Q trajectories for points along the crack fronts as load increases from small-scale yielding to large-scale yielding were obtained. Based on the materials toughness locus, (resistance to fracture JC as a function of Q), the assessments of the onset of cleavage fracture are conducted. The critical location along the 3D crack front, and the corresponding maximum load carrying capacity are obtained. The results are consistent with experimental observations. It is demonstrated the J-Q two-parameter approach is capable of providing comprehensive assessments of cleavage fracture of surface cracked plates under uniaxial/biaxial loadings, capturing all the important aspects of the problem.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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