CMOD Compliance of B×B Single Edge Bend Specimens

2012 ◽  
Author(s):  
Guowu Shen ◽  
William R. Tyson ◽  
James A. Gianetto
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Crack Depth ◽  
Mouth Opening ◽  
Crack Size ◽  
Effective Modulus ◽  
Crack Mouth Opening Displacement ◽  
Resistance Testing ◽  
Single Edge ◽  
Size Evaluation

In ASTM standard E1820, the single edge bend (SE(B)) geometry is one of those recommended for fracture toughness testing. The width to thickness (W/B) ratio recommended in E1820 for this specimen is 2. However, in certain cases, it is desirable to use specimens having alternative W/B ratios; the range of W/B suggested in E1820 is 1 to 4. In E1820, the crack size a may be evaluated during J-integral or CTOD resistance testing using the crack mouth opening displacement (CMOD) elastic unloading compliance C. The equation given to relate a to C using a dimensionless compliance BCE incorporates Young’s modulus E. For the three-dimensional (3-D) SE(B) specimens that are in neither plane stress nor plane strain condition, this parameter E may be considered as a normalizing parameter varying between extremes E (plane stress) and E/(1−ν2) (plane strain) depending on crack depth (a/W) and specimen W/B ratio. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of B×B SE(B) specimens with shallow and deep cracks and compared with that from Tada’s plane stress equation. Crack sizes evaluated using plane stress and plane strain assumptions with the 3-D CMOD compliance obtained from FEA were compared with the actual crack size of the specimens used in FEA. It was found that the errors in crack size using plane strain or plane stress assumptions can be larger than 5%, especially for shallow-cracked specimens. In the present study, an effective modulus with values between plane stress and plane strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens. The values were fitted to a polynomial equation as a function of u = 1/(√(BCE)+1) for use in estimating the dimensionless compliance for crack size evaluation for B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be significantly reduced using this effective modulus.

Dimensionless Compliance With Effective Modulus in Crack Length Evaluation for B × B Single Edge Bend Specimens

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Guowu Shen ◽  
William R. Tyson ◽  
James A. Gianetto ◽  
Jie Liang
Keyword(s):  
Fracture Toughness ◽  
Crack Length ◽  
Plane Strain ◽  
Plane Stress ◽  
Crack Size ◽  
Effective Modulus ◽  
Single Edge ◽  
Opening Displacement ◽  
Size Evaluation ◽  
Elastic Unloading

In ASTM standard E1820, the crack size, a, may be evaluated during J-integral or crack-tip opening displacement (CTOD) resistance testing using the measured crack-mouth opening displacement (CMOD) elastic unloading compliance C (UC). The equation given to relate a to dimensionless compliance BCE (the product of thickness B, the compliance C and the modulus of elasticity E) in E1820 incorporates Young's modulus E rather than the plane-strain modulus E/(1 − υ2) where υ is Poisson's ratio. However, the three-dimensional (3-D) single edge bend (SE(B)) specimens used in fracture toughness tests are in neither plane-stress nor plane-strain condition, especially for B×B SE(B) specimens which are popular in characterizing fracture toughness of pipes with surface notches. In the present study, 3-D finite element analysis (FEA) was used to evaluate the CMOD compliance of plain- and side-grooved B×B SE(B) specimens with shallow and deep cracks. Crack sizes evaluated using plane-stress and plane-strain assumptions with the CMOD compliance calculated from FEA for the 3-D specimen were compared with the actual crack size of the specimens used in FEA. It was found that the errors using plane-strain or plane-stress assumptions can be as high as 5–10%, respectively, especially for shallow-cracked specimens. In the present study, an effective modulus with value between plane-stress and plane-strain is proposed and evaluated by FEA for the 3-D B×B SE(B) specimens for use in estimating the dimensionless compliance for crack size evaluation of B×B SE(B) specimens. It is shown that the errors in crack size evaluation can be reduced to 1% and 2% for plain-sided and side-grooved specimens, respectively, using this effective modulus. The effect of material removal to accommodate integral knife edges on the CMOD compliance was studied and taken into account in the crack length evaluations in the present study. Elastic unloading tests were conducted to measure the compliance of SE(B) specimens with two widths W and notch depths a/W from 0.1 to 0.5. Notch depths of the specimens evaluated by using the measured compliance and assumptions of plane stress, plane strain, and effective moduli were compared with the notch depths of the specimens used in the tests. It was found that best agreement of notch depth was achieved using the effective modulus.

Effect of Side Grooves on Compliance, J-Integral and Constraint of a Clamped SE(T) Specimen

2010 ◽  
Author(s):  
Guowu Shen ◽  
William R. Tyson ◽  
James A. Gianetto ◽  
Dong-Yeob Park
Keyword(s):  
Plane Strain ◽  
Crack Depth ◽  
Mouth Opening ◽  
Crack Tip ◽  
Crack Mouth Opening Displacement ◽  
J Integral ◽  
Single Edge ◽  
Opening Displacement ◽  
Element Analysis ◽  
Crack Tip Constraint

The effect of side grooves on crack mouth opening displacement (CMOD) compliance, distribution of J-integral and crack-tip constraint parameters Q and A2 along the thickness of a clamped single-edge-notched tension (SE(T)) specimen were studied by finite element analysis (FEA). Focus was on the effect of depth of side grooves on J-integral and constraint parameters Q and A2 for shallow and deep cracks. The 3-D results were compared with those of SE(T) specimens in plane strain. The results show that the effective thickness equation used in ASTM E 1820 to evaluate compliance of side-grooved SE(B) and C(T) specimens can be used for clamped SE(T) specimens with reasonable accuracy. The results also suggest that the depth of the side grooves affects the distribution of the J-integral: the highest J-integral is at the center of the thickness for a SE(T) specimen with side grooves equal to or less than 10% of total thickness, and near the root of the side grooves for side grooves greater than 10% for a deeply-cracked specimen when the applied load P≥PY. The FEA results also show that the depth of side grooves affects the distribution of the constraint parameters: the crack-tip constraint is highest at the center of the thickness for a specimen with 0% side grooves (plain-sided), and near the root of the side grooves for side grooves equal to or greater than 10%. It was also found from FEA that the crack-tip constraint of a SE(T) specimen with 20% side grooves with shallow (a/W = 0.2) or deep (a/W = 0.5) crack is higher than that of a SE(T) specimen with the same crack depth in plane strain. As a result, the J-resistance of a SE(T) specimen with 20% side grooves may be lower than that of the same specimen in plane strain.

Improved Compliance Solutions for C(T), SE(B) and Clamped SE(T) Specimens Including Side-Grooves, Varying Thicknesses and 3-D Effects

2014 ◽  
Author(s):  
Gustavo Henrique B. Donato ◽  
Felipe Cavalheiro Moreira
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Plane Stress ◽  
Potential Drop ◽  
Crack Size ◽  
Growth Conditions ◽  
Size Estimation ◽  
Unloading Compliance ◽  
Integrity Assessments ◽  
Elastic Unloading

Fracture toughness and Fatigue Crack Growth (FCG) experimental data represent the basis for accurate designs and integrity assessments of components containing crack-like defects. Considering ductile and high toughness structural materials, crack growing curves (e.g. J-R curves) and FCG data (in terms of da/dN vs. ΔK or ΔJ) assumed paramount relevance since characterize, respectively, ductile fracture and cyclic crack growth conditions. In common, these two types of mechanical properties severely depend on real-time and precise crack size estimations during laboratory testing. Optical, electric potential drop or (most commonly) elastic unloading compliance (C) techniques can be employed. In the latter method, crack size estimation derives from C using a dimensionless parameter (μ) which incorporates specimen’s thickness (B), elasticity (E) and compliance itself. Plane stress and plane strain solutions for μ are available in several standards regarding C(T), SE(B) and M(T) specimens, among others. Current challenges include: i) real specimens are in neither plane stress nor plane strain - modulus vary between E (plane stress) and E/(1-ν2) (plane strain), revealing effects of thickness and 3-D configurations; ii) furthermore, side-grooves affect specimen’s stiffness, leading to an “effective thickness”. Previous results from current authors revealed deviations larger than 10% in crack size estimations following existing practices, especially for shallow cracks and side-grooved samples. In addition, compliance solutions for the emerging clamped SE(T) specimens are not yet standardized. As a step in this direction, this work investigates 3-D, thickness and side-groove effects on compliance solutions applicable to C(T), SE(B) and clamped SE(T) specimens. Refined 3-D elastic FE-models provide Load-CMOD evolutions. The analysis matrix includes crack depths between a/W=0.1 and a/W=0.7 and varying thicknesses (W/B = 4, W/B = 2 and W/B = 1). Side-grooves of 5%, 10% and 20% are also considered. The results include compliance solutions incorporating all aforementioned effects to provide accurate crack size estimation during laboratory fracture and FCG testing. All proposals revealed reduced deviations if compared to existing solutions.

Wide Range Compliance Solutions for Various Fracture Test Specimens Using Crack Mouth Opening Displacement

2017 ◽  
Author(s):  
Claudio Ruggieri ◽  
Rodolfo F. de Souza
Keyword(s):  
Mouth Opening ◽  
Crack Mouth Opening Displacement ◽  
Width Ratio ◽  
Fracture Test ◽  
Single Edge ◽  
Opening Displacement ◽  
Element Analysis ◽  
Single Edge Notch ◽  
Wide Range ◽  
Edge Notch

This work addresses the development of wide range compliance solutions for tensile-loaded and bend specimens based on CMOD. The study covers selected standard and non-standard fracture test specimens, including the compact tension C(T) configuration, the single edge notch tension SE(T) specimen with fixed-grip loading (clamped ends) and the single edge notch bend SE(B) geometry with varying specimen spam over width ratio and loaded under 3-point and 4-point flexural configuration. Very detailed elastic finite element analysis in 2-D setting are conducted on fracture models with varying crack sizes to generate the evolution of load with displacement for those configurations from which the dependence of specimen compliance on crack length, specimen geometry and loading mode is determined. The extensive numerical analyses conducted here provide a larger set of solutions upon which more accurate experimental evaluations of crack size changes in fracture toughness and fatigue crack growth testing can be made.

TEST STUDY ON THE BEST PASTING LAYER OF FRP REINFORCED CONCRETE

2019 ◽  
Vol 27 (02) ◽  
pp. 1950105
Author(s):  
XIANGQIAN FAN ◽  
JUEDING LIU
Keyword(s):  
Fracture Toughness ◽  
Acoustic Emission ◽  
Reinforced Concrete ◽  
Crack Depth ◽  
Mouth Opening ◽  
Bending Test ◽  
Crack Mouth Opening Displacement ◽  
Displacement Curve ◽  
Crack Mouth ◽  
Opening Displacement

To optimize the strengthening method using the fiber reinforced polymer (FRP) for the reinforcement of the concrete structure with cracks, the three-point bending test was conducted on the concrete beams wrapped with different layers of FRP materials. The strain gauges were pasted on the surface of the specimens to measure the initial cracking load. The crack mouth opening displacement (CMOD) was utilized to test the load–crack mouth opening displacement curve. According to the improved calculation formula of the fracture toughness, the critical effect crack length [Formula: see text], initiation fracture toughness [Formula: see text] and instability fracture toughness [Formula: see text] of specimens were calculated. The test results showed that, under the same initial crack depth, the peak load of FRP reinforced concrete decreases with the increase of FRP pasting layer. When there was one layer wrapped over the specimen, the instability toughness of the specimen reached the maximum value and the crack resistance was the best. Based on acoustic emission testing method, the acoustic emission parameters of the above-mentioned concrete during fracture process were identified and collected. The optimal layer of the FRP reinforced concrete with cracks was analyzed from the acoustic emission method.

Comparison of J-Integral Measurement Methods on Clamped Single-Edge Notched Tension Specimens

2016 ◽  
Author(s):  
Timothy S. Weeks ◽  
Jeffrey W. Sowards ◽  
Ross A. Rentz ◽  
David T. Read ◽  
Enrico Lucon
Keyword(s):  
Mouth Opening ◽  
Surface Strain ◽  
Image Correlation ◽  
Crack Mouth Opening Displacement ◽  
J Integral ◽  
Crack Mouth ◽  
Single Edge ◽  
Opening Displacement ◽  
Strain Gradients

This paper reports an extension of a previous study that compared methods of evaluating J by the crack mouth opening displacement and by surface strain gradients. Here, the surface strain gradients are measured by three-dimensional digital image correlation. The results herein represent a small test matrix that involved evaluation of the J-integral for clamped single-edge notched tensile specimens from API 5L X65 base-metal, weld metal and the adjacent heat affected zone; the J-integral was evaluated by a standardized procedure utilizing the crack mouth opening displacement (CMOD) and by the contour integral method on an external surface strain contour. Digital image correlation provides sufficient full-field strain data for use by this method and is considerably more robust than surface-mounted strain gage instrumentation. A series of validity checks are presented that demonstrate that the data are useful and valuable. Experimental determination of the J-integral is not limited to thoroughly analyzed test geometries and may be achieved with limited instrumentation. Furthermore, the method described does not require a determination of crack size nor any instrumentation that requires access to the crack mouth.

Relationship Between J and CTOD in SE(T) and SE(B) Specimens for Stationary and Growing Cracks

2014 ◽  
Author(s):  
Diego F. B. Sarzosa ◽  
Claudio Ruggieri
Keyword(s):  
Crack Growth ◽  
Mouth Opening ◽  
Crack Growth Resistance ◽  
Plastic Work ◽  
Crack Mouth Opening Displacement ◽  
Resistance Testing ◽  
Opening Displacement ◽  
Engineering Structures ◽  
Resistance Curves ◽  
Load Displacement

Current defect assessment procedures of large engineering structures, including pipeline systems and their welded components such as field girth welds, employ crack growth resistance curves in terms of J-resistance or CTOD-resistance curves. Standardized techniques for crack growth resistance testing of structural steels are based upon laboratory measurements of load-displacement records and adopt two related estimation formulas for fracture toughness values: 1) estimating J from plastic work based on crack mouth opening displacement (CMOD), and 2) determining the CTOD value from first evaluating the plastic component of J using the plastic work defined by the area under the load vs. CMOD curve and then converting it into the corresponding value of plastic CTOD. This work addresses an investigation on the relationship between J and CTOD for three-point SE(B) and clamped SE(T) fracture specimens based upon extensive numerical analyses conducted for crack configurations with varying crack sizes. These analyses include stationary and crack growth plane-strain results to determine J and CTOD for the cracked configurations based on load-displacement records. The numerical computations show strong similarities between the J-CTOD relationship for stationary and growth analysis with important implications for experimental measurements of CTOD-resistance curves. The study provides a body of results which enables establishing accurate relationships between J and CTOD for use in testing protocols for toughness measurements.

Effects of Side-Grooves and 3-D Geometries on Compliance Solutions and Crack Size Estimations Applicable to C(T), SE(B) and Clamped SE(T) Specimens

2013 ◽  
Author(s):  
Gustavo Henrique B. Donato ◽  
Felipe Cavalheiro Moreira
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Dimensionless Parameter ◽  
Optical Measurement ◽  
Potential Drop ◽  
Crack Size ◽  
Size Estimation ◽  
Integrity Assessment ◽  
Unloading Compliance ◽  
Elastic Unloading

Engineering procedures for design and integrity assessment of structural components containing crack-like defects are highly dependent on accurate fracture toughness and Fatigue Crack Growth (FCG) experimental data. Considering ductile and high toughness structural materials, crack growing curves (e.g. J-R curves) and FCG data (in terms of da/dN vs. ΔK or ΔJ) assumed paramount relevance. In common, these two types of mechanical properties severely depend on real-time and precise crack size estimations during laboratory testing. Optical measurement, electric potential drop or (most commonly) elastic unloading compliance (C) techniques can be employed. In the latter method, crack size estimation derives from C using a dimensionless parameter (μ) which incorporates specimen’s thickness (B), elasticity (E) and compliance itself. Plane stress and plane strain solutions for μ are available in several standards regarding C(T), SE(B) and M(T) specimens, among others. Current challenges include: i) real specimens are in neither plane stress nor plane strain-modulus vary between E (plane stress) and E/(1−ν2) (plane strain); ii) furthermore, side-grooves affect specimen’s stiffness, leading to an “effective thickness”. Results from Shen et al. and from current authors revealed deviations larger than 10% in crack size estimations following existing practices, especially for shallow cracks and side-grooved samples. In addition, compliance solutions for the emerging SE(T) specimens are not yet standardized. As a step in this direction, this work investigates 3-D and side-groove effects on compliance solutions applicable to C(T), SE(B) and clamped SE(T) specimens. Refined 3-D elastic FE-models provide Load-CMOD evolutions. The analysis matrix includes crack depths between a/W = 0.1 and a/W = 0.7 on 1/2T, 1T and 2T geometries. The 1T geometry is taken as the reference and presents width to thickness ratio W/B = 2. Side-grooves of 5%, 10% and 20% are considered. The results include compliance solutions incorporating 3D and side-groove effects to provide accurate crack size estimation during laboratory fracture and FCG testing. The proposals were verified against current standardized solutions and deviations were strongly reduced.

On Fracture Mechanics Testing Technique Based on Compliance of Specimens

2008 ◽  
Vol 385-387 ◽  
pp. 293-296 ◽  
Author(s):  
Li Xun Cai ◽  
Lei Jin ◽  
Chen Bao
Keyword(s):  
Crack Length ◽  
Crack Opening ◽  
Mouth Opening ◽  
Crack Mouth Opening Displacement ◽  
Single Edge ◽  
Plastic Part ◽  
Opening Displacement ◽  
Testing Technique ◽  
Load Line ◽  
Compliance Testing

Based on compliance testing of a straight-notch compact tensile (SN-CT) or a single edge bending (SEB) specimen, this paper present a formula with increment form to calculate plastic part of J-integral, two formulas for a SN-CT specimen and a SEB specimen to transform crack mouth opening displacement (CMOD) v0 to the crack opening displacement (COD) q along load line, and simplified formulas to estimate crack length a and effective young’s modulus E. Furthermore, the relation between v and q of the SN-CT specimens of 45 steel and SEB specimens of 30Cr steel were investigated. The results show that the formulas to describe the relation between the ratio v/q and the dimensionless crack length a/w of the specimens accord with the testing results better.

Evaluation of Fracture Toughness of X100 Pipe Steel Using SE(B) and Clamped SE(T) Single Specimens

2010 ◽  
Author(s):  
Dong-Yeob Park ◽  
William R. Tyson ◽  
James A. Gianetto ◽  
Guowu Shen ◽  
Robert S. Eagleson
Keyword(s):  
Crack Length ◽  
Crack Front ◽  
Room Temperature ◽  
Pipe Steel ◽  
Crack Mouth Opening Displacement ◽  
Resistance Testing ◽  
Single Edge ◽  
Aspect Ratios ◽  
Resistance Curves ◽  
Unloading Compliance

J-resistance testing using a single-specimen unloading compliance technique has been performed on single-edge-notched tension (SE(T)) specimens of X100 pipe steel base material at room temperature and at −20°C, using a procedure developed at CANMET. J-resistance testing using single-edge-notched bend (SE(B)) specimens according to ASTM E1820 was also conducted for comparison. The specimens included two nominal through-thickness pre-crack aspect ratios (a/W = 0.25 and 0.5). The results show that shallow-cracked (a/W∼0.25) bend and tension specimens produce higher resistance curves than deeply-cracked (a/W∼0.5) specimens; ductile propagation was observed at both temperatures. Resistance curves are slightly higher at −20°C than at room temperature for both bending and tension, especially for shallow-cracked specimens. Crack length predicted from unloading compliance of crack mouth opening displacement for the SE(T) specimens was validated by optical measurement of initial crack length (ao) and final crack extension (Δa>1.0 mm) after heat-tinting, as per ASTM E1820. Predicted crack growths show acceptable agreement with measured values in all cases. The effect of side-groove depth on the resistance curve and straightness of the crack front was briefly investigated. For both bending and tension, resistance curves for 10% (total) side-grooved specimens were close to those from plain-sided specimens when other testing conditions, such as precrack and testing temperature, were the same, whereas 20% (total) side-grooved specimens showed lower toughness. It was occasionally observed that the crack grew faster at the side for 20% side-grooved bend and tension specimens, resulting in a crack front of concave curvature. For 10% side-grooved specimens a rather straight crack front or slightly faster crack growth in the middle of the specimen (convex curvature) was observed.

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