scholarly journals A Simplified SSY Estimate Method to Determine EPFM Constraint Parameter for Sensor Design

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 717
Author(s):  
Ping Ding ◽  
Xin Wang
Keyword(s):  
Loading Condition ◽  
Biaxial Loading ◽  
External Loading ◽  
Small Scale ◽  
Cracked Plate ◽  
T Stress ◽  
Estimate Method ◽  
Parameter Values ◽  
Parameter Approach ◽  
Two Parameter

To implement a sensor structure analysis and design (as well as other engineering applications), a two-parameter approach using elastic–plastic fracture mechanics (EPFM) could be applied to analyze a structure more accurately than a one-parameter approach, especially for structures with low crack constraint. The application of the J-A two-parameter approach on sensors and other structures depends on the obtainment of a constraint parameter A. To conveniently and effectively obtain the A parameter values, the authors have developed a T-stress-based estimate method under a small-scale yielding (SSY) condition. Under a uniaxial external loading condition, a simplified format of the T-stress-based estimate has been proposed by the authors to obtain the parameter A much more conveniently and effectively. Generally, sensors and other practical engineering structures endure biaxial external loading instead of the uniaxial one. In the current work, the simplified formation of the estimate method is extended to a biaxial loading condition. By comparing the estimated A parameter values with their numerical solutions from a finite element analysis (FEA) results, the extension of the simplified formation of T-stress-based estimate method to biaxial loading was discussed and validated. The comparison procedure was completed using a wide variety of materials and geometrical properties on three types of specimens: single edge cracked plate (SECP), center cracked plate (CCP), and double edge cracked plate (DECP).

scholarly journals 3D SSY Estimate of EPFM Constraint Parameter under Biaxial Loading for Sensor Structure Design

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 735
Author(s):  
Ping Ding ◽  
Xin Wang
Keyword(s):  
Fracture Mechanics ◽  
Biaxial Loading ◽  
Structure Design ◽  
Theoretical Research ◽  
Small Scale ◽  
Validation Process ◽  
Wide Range ◽  
Sensor Structure ◽  
Estimate Method ◽  
Parameter Approach

Conventional sensor structure design and related fracture mechanics analysis are based on the single J-integral parameter approach of elastic-plastic fracture mechanics (EPFM). Under low crack constraint cases, the EPFM one-parameter approach generally gives a stress overestimate, which results in a great cost waste of labor and sensor components. The J-A two-parameter approach overcomes this limitation. To enable the extensive application of the J-A approach on theoretical research and sensor engineering problem, under small scale yielding (SSY) conditions, the authors developed an estimate method to conveniently and quickly obtain the constraint (second) parameter A values directly from T-stress. Practical engineering application of sensor structure analysis and design focuses on three-dimensional (3D) structures with biaxial external loading, while the estimate method was developed based on two-dimensional (2D) plain strain condition with uniaxial loading. In the current work, the estimate method was successfully extended to a 3D structure with biaxial loading cases, which is appropriate for practical sensor design. The estimate method extension and validation process was implemented through a thin 3D single edge cracked plate (SECP) specimen. The process implementation was completed in two specified planes of 3D SECP along model thickness. A wide range of material and geometrical properties were applied for the extension and validation process, with material hardening exponent value 3, 5 and 10, and crack length ratio 0.1, 0.3 and 0.7.

scholarly journals Estimation of C∗-Integral for Central Cracked Plate Under Biaxial Loading

2020 ◽  
Vol 12 (07) ◽  
pp. 2050079
Author(s):  
Yanwei Dai ◽  
Fei Qin ◽  
Yinghua Liu ◽  
Weizhe Feng ◽  
Guian Qian
Keyword(s):  
Loading Condition ◽  
Biaxial Loading ◽  
Classical Method ◽  
Creep Crack ◽  
Cracked Plate ◽  
Reference Stress ◽  
Creep Time ◽  
Relationship Of ◽  
The Relationship ◽  
Better Than

The reference stress method (RSM) is a classical method to estimate [Formula: see text]-integral of creep crack. An extended reference stress method (ERSM) is given for the central cracked plate (CCP) under biaxial loading in this paper. The applicability and verification for the proposed ERSM is given. The study finds that the solutions with the proposed ERSM agree better than those of RSM under biaxial loading condition. A theoretical form to predict the relationship of [Formula: see text]-integral between biaxial loading and uniaxial loading is discussed. Relation between [Formula: see text]-integral and creep time under biaxial loading is validated and discussed.

Two Parameter J-A Estimation for Weld Centerline Cracks in Welded Single-Edge Cracked Plate Under Tensile Loading

2019 ◽  
Author(s):  
Chuanjie Duan ◽  
Shuhua Zhang
Keyword(s):  
Large Scale ◽  
Tensile Loading ◽  
Small Scale ◽  
Material Strength ◽  
Single Edge ◽  
Weld Width ◽  
Elastic Plastic ◽  
Cracked Plate ◽  
Scale Yielding ◽  
Two Parameter

Abstract This work examines the J–A two-parameter characterization of elastic–plastic crack front fields for weld centerline cracks under tensile loading. Extensive finite element analyses (FEA) have been conducted to obtain solutions of constraint parameter A, which is the second parameter in a three-term elastic-plastic asymptotic expansion for the stress field near the tip of mode-I crack, for modified boundary layer (MBL) model and welded single-edge cracked plate (SECP). Solutions of the constraint parameter A were obtained for the material following the Ramberg-Osgood power law. The crack geometries analyzed include shallow and deep cracks, and remote tension loading levels cover from small-scale to large-scale yielding conditions. The effects of weld material mismatch and weld width on crack tip constraint were considered in the FEA. A constraint parameter AM, only caused by material strength mismatch, is defined and its parametric equation was obtained. The total constraint in the bi-material weldment can be predicted by adding together AM and A in the homogeneous material. Good agreements were achieved for welded SECP specimen with different crack size and weld width from small-scale to large-scale yielding conditions. This methodology would be useful for performing constraint-based elastic-plastic fracture analyses of other welded test specimens.

T-stress estimation by the two-parameter approach for a specimen with a V-shaped notch

2017 ◽  
Vol 58 (3) ◽  
pp. 546-555 ◽  
Author(s):  
O. Bouledroua ◽  
A. Elazzizi ◽  
M. Hadj Meliani ◽  
G. Pluvinage ◽  
Y. G. Matvienko
Keyword(s):  
T Stress ◽  
Stress Estimation ◽  
Parameter Approach ◽  
Two Parameter

Creep Analysis and Constraint Effect in a Center-Cracked Plate Under Biaxial Loading

2014 ◽  
Author(s):  
Zhongxian Wang ◽  
Yan-qing Zhang ◽  
Poh-Sang Lam ◽  
Yuh J. Chao
Keyword(s):  
Biaxial Loading ◽  
Crack Tip ◽  
Pressure Vessels ◽  
Contour Integral ◽  
Small Scale ◽  
Crack Tip Field ◽  
Cracked Plate ◽  
Creep Analysis ◽  
Creep Time ◽  
Crack Tip Constraint

Typical pressure vessels are subject to biaxial loading. Creep analysis was conducted with two-dimensional finite element method for a center-cracked plate under a range of biaxial loading ratios (λ = −1, 0, and 0.5). The effects of crack size and the biaxial loading ratio on the crack tip field are reported. In addition, based on a two-parameter fracture theory, C(t)−A2(t), where C is a contour integral and is path-independent when the steady state creep is reached (denoted by C*), and A2 is a time dependent crack tip constraint parameter. The crack tip stress field calculated from the C(t)−A2(t) theory is shown to be more accurate than the Hutchinson–Rice–Rosengren (HRR) singularity solution, especially in the case of λ = 0.5. The loading level appears to have little effects on the constraint parameter A2(t). As creep time increases, the creep zone (based on the equivalent creep strain) increases rapidly but the yield zone (with respect to a reference stress) decreases. Meanwhile, the crack tip constraint is increasing with creep time, particularly for the small cracks. It was also found that the normalized relationship between the contour integral C(t)/C* and the creep time t/tT (where tT is the characteristic time for transition from small-scale creep to extensive creep) is insensitive to the biaxial loading. Therefore, the relationship previously provided for uniaxial loading can be used for biaxial loading.

Constraint of Semi-Elliptical Surface Cracks in T and L-Joints

2006 ◽  
Vol 326-328 ◽  
pp. 939-944
Author(s):  
Hyung Yil Lee ◽  
Yun Jae Kim
Keyword(s):  
Finite Element ◽  
Structural Characteristics ◽  
Pressure Vessels ◽  
Surface Cracks ◽  
Spring Model ◽  
Constraint Effect ◽  
T Stress ◽  
Line Spring Model ◽  
Parameter Approach ◽  
Two Parameter

Critical defects in pressure vessels and pipes are generally found in the form of a semielliptical surface crack, and the analysis of which is consequently an important issue in engineering fracture mechanics. Furthermore, in addition to the traditional single parameter K or J-integral, the second parameter like T-stress should be measured to quantify the constraint effect. In this work, the validity of the line-spring model is investigated by comparing line-spring J-T solutions to the reference 3D finite element J-T solutions. A full 3D-mesh generating program for semi-elliptical surface cracks is employed to provide such reference 3D solutions. Then some structural characteristics of the surface-cracked T and L-joints are studied by mixed mode line-spring finite element. Negative T-stresses observed in T and L-joints indicate the necessity of J-T two parameter approach for analyses of surface-cracked T and L-joints.

Evaluation of Fracture Toughness Behavior of SA508 Steel Considering Biaxial Loading Condition

2012 ◽  
Author(s):  
Jong-Min Kim ◽  
Ki-Hyoung Lee ◽  
Ho-Jin Lee ◽  
Bong-Sang Lee
Keyword(s):  
Fracture Toughness ◽  
Finite Element ◽  
Loading Condition ◽  
Biaxial Loading ◽  
Small Scale ◽  
Constraint Effect ◽  
Integrity Assessment ◽  
Cruciform Specimen ◽  
Elastic Plastic ◽  
Deep Crack

The crack-tip stress field and fracture mechanics assessment parameters, such as the elastic stress intensity factor and the elastic-plastic J-integral, for a surface crack can be significantly affected by the loading condition and crack geometry. Current guidance considers that the ductile-to-brittle transition is defined using uniaxially loaded specimens with a deep crack even when the reactor pressure vessel is under biaxial loading and the existence of deep crack is not probable through periodic in-service-inspection. Thus, such a constraint effect caused by differences between standard specimens and a real structure can overestimate the fracture toughness and affects the results of the structural integrity assessment. The present paper investigates the constraint effect by evaluating the Mater Curve T0 reference temperature of PCVN (Pre-cracked Charpy V-Notch) and small scale cruciform specimens of SA508 Gr. 3 low alloy steel through the fracture toughness tests of theses specimens and 3-dimensional elastic-plastic finite element analyses. Based on the finite element results, the fracture toughness values of a small-scale cruciform specimen were estimated, and the geometry-dependent factors of the cruciform specimen considered in the present study were determined and then the transferability of the test results of these specimens were discussed.

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.

Evaluation of T Stress for a Finite Internally Cracked Plate by Using EEVM Method

1997 ◽  
Vol 145-149 ◽  
pp. 47-50
Author(s):  
Yan Hong Chen ◽  
Yan Bin Luo ◽  
Xiao Yan Lin
Keyword(s):  
Cracked Plate ◽  
T Stress
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