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.

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.

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.

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.

A Numerical Study on CMOD Compliance for Single-Edge Notched Bending Specimens

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Enyang Wang ◽  
Wenxing Zhou ◽  
Guowu Shen ◽  
Daming Duan
Keyword(s):  
Crack Length ◽  
Plane Strain ◽  
Plane Stress ◽  
Stress Condition ◽  
Three Dimensional ◽  
Plane Strain Condition ◽  
Strain Condition ◽  
Two Dimensional ◽  
Single Edge ◽  
Plane Stress Condition

Several well-known equations for estimating the crack length in the single-edge notched bending (SE(B)) specimens from the normalized crack mouth opening displacement (CMOD) compliance are evaluated based on two-dimensional (2D) and three-dimensional (3D) finite element analyses (FEAs). Two-dimensional FEAs are first carried out to verify the reported accuracy and applicable ranges for each equation based on the plane strain models with six different crack lengths. Three-dimensional FEAs are then carried out to estimate the errors of prediction of equations that evaluate the crack length from the plane stress- and plane strain-based CMOD compliances. Both plane-sided and side-grooved models are included in 3D FEAs and have seven different thickness-to-width ratios. The error of prediction of a given equation is largely impacted by the thickness-to-width ratio, the crack length, the presence of side grooves, and the use of the plane stress- or plane strain-normalized CMOD compliance. Based on the errors of prediction, the relevance of the actual state of stress in the ligament of the SE(B) specimens to the plane strain condition or the plane stress condition is inferred. Knowledge of the relevance of the plane stress condition or the plane strain condition can be used to select the corresponding CMOD compliance in crack length-CMOD equations, and, therefore, the corresponding predictive accuracy can be improved.

The influence of crack size on the ductile-brittle transition

1988 ◽  
Vol 415 (1848) ◽  
pp. 197-226 ◽  
Keyword(s):  
Boundary Layer ◽  
Fracture Toughness ◽  
Transition Temperature ◽  
Plane Strain ◽  
Crack Size ◽  
Specimen Geometry ◽  
External Loading ◽  
Stress And Strain ◽  
Strain Fields ◽  
Penny Shaped Crack

Simple criteria for brittle and ductile crack extension are applied to the stress and strain fields adjacent to the tip of a crack. They are applied at a specified distance from the crack tip, which should be related to the material’s microstructure. The basic approach is to examine each criterion and find which is satisfied first, as the external loading is increased; the predicted fracture is classified either brittle or ductile accordingly. The stress and strain fields depend upon temperature, principally through the variation of flow stress σ 0 with temperature and, to avoid excessive computation, a constitutive relation is constructed which allows stresses and strains both to be scaled in terms of σ 0 , so that major computations need to be done only at a reference temperature, for a range of applied loads. For any given crack configuration, the result of the calculation is a theoretical prediction of fracture toughness as a function of temperature. At low temperatures, the fracture toughness is low and rises rapidly with temperature, corresponding to satisfaction of the criterion for brittle failure. Above a transition temperature, T T , the ductile criterion is satisfied first, and the toughness variation thereafter falls slowly as temperature increases, corresponding to failure ‘on the upper shelf’. Both the absolute level of the toughness at a given temperature and the transition temperature T T are sensitive to crack size as well as specimen geometry. Although this is self-evident for cracks of microstructural dimensions, the striking feature of this work is the prediction that substantial sensitivity to size and geometry may well be displayed for cracks as large as 1 cm in materials of significance for major engineering structures. Generally, toughness increases and transition temperature decreases as crack size decreases, but these beneficial effects can be nullified by stress triaxiality. Detailed calculations are performed for a buried crack and an edge crack under conditions of plane strain and for a penny-shaped crack loaded axisymmetrically. The plane strain calculations are supplemented by ‘boundary layer’ calculations, in which the effect of specimen geometry appears through a single parameter. The close agreement of the ‘boundary layer’ calculations with the full specimen calculations offers the prospect of a simple characterization of specimen geometry and loading, without the need for geometry-specific computations. The calculations that are reported are, of course, based upon a particular model, chosen in part for com­putational convenience. Thus, their status is that they display possible trends which may be considered to merit further investigation, both theoretical and experimental.

Single Edge Precrack V-Notched Beam (SEPVNB) Fracture Toughness Testing on Silicon Nitride

2019 ◽  
Vol 962 ◽  
pp. 205-209
Author(s):  
Tjokorda Gde Tirta Nindhia ◽  
Tanja Lube
Keyword(s):  
Fracture Toughness ◽  
Silicon Nitride ◽  
Crack Size ◽  
Fracture Toughness Test ◽  
Single Edge ◽  
Razor Blade ◽  
Sintered Ceramic ◽  
Toughness Test ◽  
Toughness Testing ◽  
Diamond Paste

The previous Measurement of fracture toughness test by using bright indentation for precracked beam method (ASTM C1421) was found difficult to be carried out due to difficulty in precrack generation and measurement of the crack size. In this research single edge precrack V-notch beam (SEPVNB) is introduced as an alternative to solve the problem from previous standardized method. A real crack that can created with referred size is recognized as the best condition for fracture toughness test. The material prepared for this purpose was silicon nitride (Si3N4) produced by CeramTec (Plochingen, Germany) under the name SL200 B. It is a gas pressure sintered ceramic containing 3 wt.% Al2O3 and 3 wt.% Y2O3. The V Notch was prepared by using razor blade with diamond paste following ISO/FDIS 23146 standard preparation with more addition on precrack introduction. The precrack was introduced by so called opposite roller loading. The fracture toughness test was carried out by following procedure in ISO/FDIS 23146 . The result then was compared for validation with both single edge V-notch beam standard (ISO/FDIS 23146 ) and Surface crack in Flexure SCF (ASTM C 1421). The result of fracture toughness by using method that is introduce in this research is found 5.8270.275 MPa1/2 which is close to the result of SCF (5.335 0.222 MPa1/2). Meanwhile the value of fracture toughness by using V-notch beam is 4.9130.098 MPa1/2

Fracture Toughness of X70 Pipe Girth Welds Using Clamped SE(T) and SE(B) Single-Specimens

2014 ◽  
Author(s):  
Dong-Yeob Park ◽  
Jean-Philippe Gravel ◽  
C. Hari Manoj Simha ◽  
Jie Liang ◽  
Da-Ming Duan
Keyword(s):  
Fracture Toughness ◽  
Heat Affected Zone ◽  
Peak Load ◽  
Single Specimen ◽  
Single Edge ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Resistance Curves ◽  
Girth Welds ◽  
Crack Tip Opening

Shallow-notched single edge-notched tension (SE(T) or SENT) and deep- and shallow-notched single edge-notched bend (SE(B) or SENB) specimens with notches positioned in the weld and the heat-affected zone were tested. Crack-tip opening displacement (CTOD) versus resistance curves were obtained using both a single and double clip gauge consolidated in a SE(T) single-specimen. Up until the peak load the resistance curves from both gauging methods yield approximately the same results; thereafter the curves deviate. Interrupted testing showed that the crack had initiated below 50% of the peak load, and in some cases had propagated significantly prior to reaching the peak load.

CTOD Fracture Toughness Assessment Under Different Notch Type (Fatigue Pre-Cracking and EDM)

2019 ◽  
Author(s):  
Israel Marines-Garcia ◽  
Aaron Aguilar ◽  
Kristian Carreon ◽  
Philippe Darcis
Keyword(s):  
Fracture Toughness ◽  
Crack Length ◽  
Heat Affected Zone ◽  
Crack Tip ◽  
Fusion Line ◽  
Testing Time ◽  
Pipe Material ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Electro Discharge Machining

Abstract The standardization of any mechanical material characterization is aiming to get homogenization on the testing physical execution by independent laboratories and to drive for accurate material evaluation between different entities. However, from time to time, standard tests may be reconsidered in order to improve their efficacy, execution time and incorporate new testing techniques or technologies without compromising the testing results and consistency. In the present work, fracture toughness crack tip opening displacement (CTOD) testing is addressed and particularly the need to perform fatigue pre-cracking prior monotonic testing. Without the fatigue pre-cracking, CTOD testing time can be significantly reduced during the preparation of specimens, meaning that specimens can be tested as soon as they are machined. Wire electro-discharge machining (EDM) technique allows generating sharp tip notches, and presents a good alternative to the standards specified fatigue pre-cracking [1–2]. In addition, this machining technology reduces the risk of rejecting the specimen testing, particularly when targeting weld heat affected zone/fusion line (HAZ/FL) microstructure on specimens with surface notch DNV-ST-F101 Figure B-9 [3], where it is specified that the crack tip shall be within a narrow distance (0.5 mm) from the fusion line (FL) or assess grain coarsened heat affected zone (GCHAZ) microstructure as indicated in DNV-ST-F101 section B.2.8.7 [3]. Herein, it is presented an assessment carried out in order to identify the notch type effect over the fracture toughness (CTOD) considering notches conditions as standard fatigue pre-crack and wire electro-discharge machining (EDM). Fifteen (15) CTOD specimens were manufactured from plain pipe material (same pipe), 251.3 mm OD × 20.9 mm WT, SMLS 450PD and tested according to ISO 12135 recommendations [1], they were distributed as follow; five (5) specimens according to standard recommendations with fatigue pre-cracking length ≥ 1.3 mm or 2.5%W (whichever is bigger), five (5) specimens with a fatigue pre-cracking length < 1.3 mm (between 0.5 mm to 1 mm), and five (5) specimens without fatigue pre-cracking (EDM notch), additionally, results from five (5) specimens previously tested in a round robin (RR) testing performed internally by Tenaris using the same LP material and standard fatigue pre-crack length. The crack length target (a/W) was kept 0.5 for all cases. Even if the sampling population is relatively small considering the three notch conditions, it seems that EDM might be an alternative to the standard specified fatigue pre-cracking. Thus, this experimental assessment aims to open the discussion on the use of EDM notch as alternative.

A Numerical Study on CMOD Compliance for Single-Edge Bending Specimens

2012 ◽  
Author(s):  
Enyang Wang ◽  
Wenxing Zhou ◽  
Guowu Shen ◽  
Daming Duan
Keyword(s):  
Crack Length ◽  
Plane Strain ◽  
Plane Stress ◽  
Numerical Study ◽  
Three Dimensional ◽  
Actual State ◽  
Width Ratio ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Different Thickness

Several well-known equations for estimating the crack length in the SE(B) specimens from the normalized CMOD compliance are evaluated based on two- and three-dimensional finite element analyses. Two-dimensional analyses are carried out first to verify the reported accuracy and applicable ranges for each equation based on the plane strain models with six different crack lengths. Three-dimensional analyses are then carried out to estimate the errors of prediction of the equations that evaluate the crack length from the plane stress- and plane strain-based CMOD compliances. Both plain-sided and side-grooved models are included in the three-dimensional analyses and have seven different thickness-to-width ratios. The error of prediction of a given equation is largely impacted by the thickness-to-width ratio, crack length, presence of side grooves, and use of the plane stress- and plane strain-normalized CMOD compliance. Based on the errors of prediction, the relevance of the plane strain and plane stress conditions to the actual state of stress in the ligament of the SE(B) specimens is inferred. Knowledge of the relevance of the plane stress and plane strain conditions can be used to select either plane stress- or plane strain-based CMOD compliance in the crack length-CMOD equations and improve the accuracy of the prediction.

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