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.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals Displacement Formulations for Deformation and Vibration of Elastic Circular Torus

2021 ◽  
Author(s):  
bohua sun
Keyword(s):  
Free Vibration ◽  
Gaussian Curvature ◽  
Turning Point ◽  
Closed Form Solution ◽  
Complex Form ◽  
Form Solution ◽  
Element Analysis ◽  
Displacement Boundary ◽  
Engineering Mechanics ◽  
Maple Code

The formulation used by most of the studies on an elastic torus are either Reissner mixed formulation or Novozhilov's complex-form one, however, for vibration and some displacement boundary related problem of a torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for the torus. In this paper, I will carry on my previous work [ B.H. Sun, Closed-form solution of axisymmetric slender elastic toroidal shells. J. of Engineering Mechanics, 136 (2010) 1281-1288.], and with the help of my own maple code, I am able to simulate some typical problems and free vibration of the torus. The numerical results are verified by both finite element analysis and H. Reissner's formulation. My investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio, and suggest that the analysis of a torus should be done by using the bending theory of a shell, and also reveal that the inner torus is stronger than outer torus due to the property of their Gaussian curvature. Regarding the free vibration of a torus, our analysis indicates that both initial in u and w direction must be included otherwise will cause big errors in eigenfrequency. One of the most intestine discovery is that the crowns of a torus are the turning point of the Gaussian curvature at the crown where the mechanics' response of inner and outer torus is almost separated.

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.

Crack-tip constraint analysis of SENB specimen under creep condition

2015 ◽  
Vol 29 (2) ◽  
pp. 501-506 ◽  
Author(s):  
G. C. Jiao ◽  
W. Z. Wang ◽  
S. J. Tan ◽  
C. Yu ◽  
Y. Z. Liu
Keyword(s):  
Creep Condition ◽  
Crack Tip ◽  
Constraint Analysis ◽  
Crack Tip Constraint ◽  
Senb Specimen

Strengthening of wide-flange columns under load

1990 ◽  
Vol 17 (5) ◽  
pp. 835-843 ◽  
Author(s):  
H. Marzouk ◽  
S. Mohan
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Critical Load ◽  
Closed Form Solution ◽  
Welding Process ◽  
Form Solution ◽  
Element Analysis ◽  
Welding Stress ◽  
Existing Structures ◽  
Welding Sequence

The present work deals with formulation of theoretical and analytical methods leading to the development of column strength curves. The formulations were developed for both elastic and inelastic behaviour. Two types of reinforcement have been developed for strengthening the W-shape columns under load. Since the column strength curves are based in part on the magnitude and distribution of residual stresses, it is extremely important to consider the new pattern of residual stresses due to welding process. Also, the welding sequence will affect the magnitude and distribution of residual stresses. Theoretical formulations leading to a closed-form solution for the prediction of critical load were developed for two types of strengthening using the superposition of original residual, new welding, and initial loading stresses. A nonlinear finite element analysis based on the large deformation theory of stability was used to predict the strengthened column critical load. It takes into consideration the effect of cooling residual stresses and new welding residual stresses. The formulations were incorporated with gradual penetration of yielding, the spreading of inelastic zones along the member length, the presence of residual stresses, and strain hardening of the material. Experiments were carried out to determine the actual capacity of strengthened columns. Seven specimens were tested using two and four strengthening plates. The welding stresses were measured through a series of experiments, and it was found that the parabolic distribution is a very close approximation to the actual new welding stress distribution. Key words: reinforcement of steel columns, welding stresses, welding sequence, strengthening of existing structures, buckling, steel plating, finite element.

Using Isochronous Method to Calculate Creep Damage in Pressure Vessel Components: Part 2

2017 ◽  
Author(s):  
Chithranjan Nadarajah ◽  
Benjamin F. Hantz ◽  
Sujay Krishnamurthy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Pressure Vessel ◽  
Closed Form Solution ◽  
Creep Damage ◽  
Form Solution ◽  
Creep Model ◽  
Stress Strain ◽  
Element Analysis ◽  
Good Agreement

This paper is Part 2 of two papers illustrating how isochronous stress strain curves can be used to calculate creep stresses and damage for pressure vessel components. Part 1 [1], illustrated the use of isochronous stress strain curves to obtain creep stresses and damages on two simple example problems which were solved using closed form solution. In Part 2, the isochronous method is implemented in finite element analysis to determine creep stresses and damages on pressure vessel components. Various different pressure vessel components are studied using this method and the results obtained using this method is compared time explicit Omega creep model. The results obtained from the isochronous method is found to be in good agreement with the time explicit Omega creep model.

Effects of Temperature and Crack Tip Constraint on Cleavage Fracture Toughness in the Weld Thermal Simulated X80 Pipeline Steels

2011 ◽  
Vol 197-198 ◽  
pp. 1595-1598 ◽  
Author(s):  
Jie Xu ◽  
Yu Fan
Keyword(s):  
Fracture Toughness ◽  
Cleavage Fracture ◽  
Crack Tip ◽  
Coarse Grained ◽  
Material Microstructure ◽  
Element Analysis ◽  
Pipeline Steels ◽  
Different Temperatures ◽  
Effects Of Temperature ◽  
Crack Tip Constraint

This paper studies the effects of temperature and crack tip constraint on cleavage fracture toughness of the weld thermal simulated X80 pipeline steels. A large number of fracture toughness (as denoted by CTOD) tests together with 3D finite element analysis are performed using single edge notched bending (SENB) and tension (SENT) specimens at different temperatures. Coarse-grained heat-affected zone (CGHAZ) is considered as the material microstructure in preparation of the weld thermal simulated fracture mechanics specimens.

On the Changing Order of Singularity at a Crack Tip

1977 ◽  
Vol 44 (4) ◽  
pp. 625-630 ◽  
Author(s):  
R. J. Nuismer ◽  
G. P. Sendeckyj
Keyword(s):  
Closed Form ◽  
Stress Singularity ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Form Solution ◽  
Square Root ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
Line Inclusion ◽  
Crack Tip Stress

The nature of the transition in the crack tip stress singularity from an inverse square root to an inverse fractional power as a crack tip reaches a phase boundary or a geometrical discontinuity for interface cracks is examined. This is done by analyzing the simple closed-form solution to the problem of a rigid line inclusion with one side partially debonded for the case of antiplane deformation. For this example, the crack tip stress singularity changes from an inverse square root to an inverse three-quarters power as the crack tips approach the inclusion tips (i.e., when one face of the rigid line inclusion is completely debonded). A detailed analysis, based on series expansions of the closed-form solution, is used to show how the singularity transition occurs. Moreover, the expansions indicate difficulties that may be encountered when solving such problems by approximate methods.

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