Stephen M. Graham, PhD US Naval Academy Presented at the Sixth Symposium on Application of Automation Technology in Fatigue and Fracture Testing and Analysis
Results from analytical round-robin conducted by E1820 Task Group confirm that small differences in crack length from compliance can lead to large differences in a, and resulting uncertainty in J Ic Movement within ISO and ASTM to more clearly define uncertainty (ISO) and/or precision and bias (ASTM) in standards
Investigate how uncertainty in J Ic is related to the following factors that effect determination of compliance: Nonlinearity and range of fit for linear regression Inclusion of data from unload, reload, or both in regression Error in compliance data due to noise
measured P, v & C LL (n) Crack lengths a(n) Rotation corrected a(n) a oq Data selection Polynomial fit J(n) & a(n) J-Integral J(n) Crack ext. a(n) Data selection Power Law fit C1 & C2 J Ic Intersection with 0.2 mm offset line
Unload and reload are typically very linear Hysteresis or displacement offset may cause them not to fall on top of one another reload Fit Range unload
Non-linearity at start/end of unload/reload E1820 does not provide guidance on what data to use for calculating compliance Procedure for selecting data to avoid non-linear regions should be adopted
Y E( Y) EY ( ) o x 1 When x is force and Y is displacement, 1 is compliance When is normally distributed, then 1 is also normally distributed with mean and standard error: ˆ 1 s 1 n 1 y ˆ ˆ i ( 0 1xi) 2 2 x x i 2 Confidence interval on compliance, 1 ˆ s t, ˆ s t 1 1 * * 1 1 n2 1 n2
The Student s-t distribution can be used with the standard error of the data about the fit to generate confidence bounds provided that: There is just one independent variable, x, and one dependent variable, y. For any value of x, the y-values are independent and are normally distributed. For each value of x, the probability distribution of y has the same standard deviation. * ˆ st ˆ n 2 at confidence level 1
GJO-12A Mean and Confidence Bounds are from simple linear regression using all of the data in the UNLOAD 4000 3000 Crack Length (mm) 28 29 600 400 2000 NOTE that abscissa is crack length, not crack extension because shifting to a oq would obscure the confidence interval 1000 Unload - mean Unload - 95% Confidence Bounds 200 0 1.1 1.15 Crack Length (in) 0
Phase III Conduct Monte-Carlo Simulation to Determine Uncertainty in J Ic Resulting from variance in Compliance 3 Data selection methods: Simple linear regression of all data in UNLOAD only (UA) Simple linear regression of all data for BOTH (BA) Linear regression of Optimum Region from SDAR for UNLOAD only (UOR) Using mean and standard error for each compliance measurement, randomly sample from inverse cumulative t-distribution to get compliances. Propagate uncertainty in a through analysis to J Ic Repeat 1000 times and calculate mean, standard deviation and coefficient of variation for key parameters (a oq, C1, C2) and J Ic.
Result shown for specimen FYB-A1 is typical of results for all specimens analyzed Polynomial fit for a oq is robust and consequently variation is small 1.203 1.202 1.201 1.2 1.199 1.198 1.197 30.55 30.5 30.45 30.4 1.196 1.195 30.35 1.194 1.193 30.3 1.192 1.191 0 200 400 600 800 1000 Monte-Carlo Trial number
Results shown for 6 C(T) specimens from ASTM E1820 round robin with 3 data selection methods Cov is stddev/mean When only UNLOAD data is used, uncertainty in J Ic is less than 4% of the mean when std error of compliance is less than 0.25% of the mean for points used in power law fit cov(jic) 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 0.005 0.01 0.015 cov(cll) UOR UA BA
Increase sampling rate to get more data Ensure sufficient digital resolution Eliminate sources of noise Remove nonlinear region at start of unload, or end of reload, from regression Choose either unload only or reload only
1. Cannot make definitive recommendation of UNLOAD only or RELOAD only because quality of data is material and test system dependent. 2. Better not to use BOTH unload and reload because it increases uncertainty compared with either unload or reload only. 3. Calculation of standard error on compliance provides a useful check on the quality of the data, and can be related to uncertainty in J Ic. 4. A cov(cll) for points between exclusion lines of less than 0.0025 results in a cov(j Ic ) of less than 0.04, or the standard deviation in J Ic is less than 4% of the mean J Ic
Provide more explicit guidance on selecting range of unload/reload data for fit. Require that either unload only or reload only be used for measuring compliance. Require evaluation of test system to determine uncertainty in compliance, at least for first specimen in series of replicate tests. Set limit on standard error in compliance Add information on how uncertainty in compliance influences uncertainty in JIc to Precision and Bias statement Clarify data selection for Power Law Fit to avoid J-R curve with increasing slope (C 2 > 1)
4000 Crack Extension (mm) 0 1 2 GJO-12A 600 3000 400 2000 1000 200 Reload 0 0 0 0.05 0.1 Crack Extension (in)
Development of a Precision & Bias Statement for E1921 High Rate Annex and modifications to Section 12 E. Lucon & J. Splett - NIST, Boulder CO (USA) ASTM E08.07.06 Task Group on Ductile-to-Brittle Transition Anaheim CA, 19 th May 2015
Background A new Annex A1 to E1921 is being developed and balloted on Special Requirements for Determining the Reference Temperature, T o,x, at Elevated Loading Rates. It contains provisions previously scattered inside the main body of the Standard, plus references to Annex A17 of E1820-13 (Fracture Toughness Tests at Impact Loading Rates using Precracked Charpy- Type Specimens). Annex A1 will contain a Precision & Bias Statement developed from the statistical analysis of an interlaboratory study on the measurement of T o from impact-tested PCC specimens (IAEA CRP-8, conducted between 2006-2009). Some of the lessons learned will be used in a modification of the current Section 12 (P & B) of ASTM E1921-14a.
Interlaboratory Study considered IAEA CRP-8, Master Curve Approach to Monitor Fracture Toughness of Reactor Pressure Vessels in Nuclear Power Plants, Topic Area 2: Loading Rate Effects and Qualification of Impact Fracture Toughness Round-Robin Exercise on Impact Fracture Toughness (Dynamic Master Curve analysis) using Charpy-type precracked (PCC) specimens 10 participants 10 PCC specimens tested by each participant between -30 C and 10 C JRQ steel (A533B cl. 1) Loading rate/impact speed: 1.2 m/s. Presentation given on May 17 th, 2015 at ASTM Workshop on Fracture Toughness Testing and Evaluation at Elevated Loading Rates
Justification and Theoretical Background Data do not conform to the requirements of E691 (Standard Practice for Conducting an Interlaboratory Study to Determine the Precision of a Test Method) because T 0 and its σ do not represent typical means and σ based on repeated measurements. However, the definition of repeatability and reproducibility from E691 can be used. Each T 0 is considered to be based on a sample size of 1 for analysis purposes. Calculated standard deviations are similar, so estimates were pooled to obtain the repeatability standard deviation.
Precision Statement Statistics were calculated using the standard deviation of participants individual T 0 (calculated using Eq. 30 or E1921). One participant was excluded after being statistically identified as an outlier. Repeatability Reproducibility Number of Parameter determinations Average Repeatability Reproducibility Standard Standard Limit, r Limit, R Deviation, s r Deviation, s R T 0, C 9-0.1 7.40 A 7.40 B 20.7 20.7 Since calculated s R < s r, it is set s R = s r in accordance with E691.
Proposed modification of current E1921 Section 12 (Precision and Bias) Proposal: simplify, improve, and correct the estimates of repeatability and reproducibility for both single-t and multi-t methods of estimating T 0. Rationale a) New analysis is simpler than current analysis. b) It corresponds to E691 for the special case where each lab supplies a single T 0 and its associated uncertainty (eq. 30). c) Paule-Mandel method is no longer needed. d) Will be consistent with the P & B analysis of elevated loading rate data (proposed Annex A1).
Modified Section 12 Single T CURRENT REVISED Multi T CURRENT REVISED
E1921 front face correction ASTM E08 Nov. 2014 Kim Wallin VTT Technical Research Centre of Finland
E1921 front face correction 7.1 When front face (at 0.25W in front of the load-line) displacement measurements are made with the Test Method E399 design, the load-line displacement can be inferred by multiplying the measured values by the constant 0.73. Originally intended to correct for small plasticity in old K IC test results. 8.2.3 Follow Test Method E1820, 8.5 for crack size measurement, 8.3.2 for testing compact specimens. 8.6.2 The elastic modulus to be used should be the nominally known value, E, for the material 8.6.3 All calculated crack sizes should be within 10 % of the visual average 15/05/2015 2
Rotational point of C(T) specimen 0.6 FEM C(T) H/W = 0.6 LL a/wr (1a/W) a/wr 1a/W x/w X r p, r e 0.4 0.2 r p 0.43 Bao Khan McMeeking Hu Wu r 0.13 0.43 x xp xp for the plastic displacement x = xp and LL = LLp x Saxena & Hudak r e 0.13 0.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a/w 15/05/2015 3
Correction of compliance AC X CLL 0.20 a / W 0.975, 0 x 0.35W Ax/W x a x a A 1.07 0.976 0.35 4.056 W W W W 3 4 x a x a 2.874 8.981 4.99 10.23 W W W W x a 2.547 4.318 W W 5 2 Based on Saxena and Hudak for x/w = 0 0.345 15/05/2015 4
Accuracy of compliance correction C L L-est.x /C LL-E1820 1.010 1.005 1.000 0.995 E1820 x/w = 0.345 x/w = 0.25 x/w = 0.1576 Saxena and Hudak 0.990 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a/w 15/05/2015 5
Correction of compliance 1.010 1.005 x/w = 0.345 x/w = 0.25 x/w = 0.1576 C LL-est.x /C LL 1.000 0.995 E1820 x 0.0244 0.704 Cx a x a x a W x a 0.9652 0.00831 2.6106 2.325 4.617 C a LL W W W W W W W W 0.990 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 a/w 3 2 Based on Saxena and Hudak for x/w = 0 0.345 15/05/2015 6
E1921 should use Plastic correction for Ap and Complinace correction for compliance 0.80 0.75 a a MP 0.6407 0.2463 0.0197 W W 2 Multiplier 0.70 0.65 E1921 a a MC 0.35210.8752 0.04588 W W a x 0.3 0.7 0.25 W W 2 0.60 Elastic part Plastic part Compliance 0.55 0.3 0.4 0.5 0.6 0.7 a/w 15/05/2015 7
TECHNOLOGY FOR BUSINESS
Two-and Three-Dimensional Finite-Element Fracture Simulations on Metallic Materials using the Critical CTOA Fracture Criterion J.C. Newman, Jr., J.M Warren and O.M. Mahtabi Department of Aerospace Engineering Mississippi State University Mississippi State, MS ASTM E08.07.07 CTOA and 5 Task Group 18 May 2015 Anaheim, CA Outline of Presentation Finite-element fracture simulations using ZIP3D and critical CTOA fracture criterion on 7249 aluminum m alloy Notch-Strength Analysis and Fracture Mechanics Comparisons with Two-Parameter Fracture Criterion Finite-element fracture simulations using ZIP2D (plane-strain core) and critical CTOA fracture criterion on 2219 aluminum alloy Comparisons with Two-Parameter Fracture Criterion Concluding Remarks E08.07.07 # 2 ASTM May 2015 1
Capabilities of the ZIP3D Code Elastic or Elastic-Plastic Finite-Element code Element type: - Isoparametric (8-noded) element Classical Plasticity Material Non-Linearity: - Prandl-Reuss-Drucker & Zienkiewicz - Elastic-perfectly plastic, bilinear, multi-linear or - Ramberg-Osgood stress-strain curve Hardening: Isotropic or Kinematic Fatigue and Fracture: - Calculate crack-tip parameters K or J - Stable crack growth using CTOA (or CTOD) - Cyclic crack growth and crack closure E08.07.07 # 3 Crack Configurations Tested and Analyzed E08.07.07 # 4 ASTM May 2015 2
One-Quarter of Non-Standard Compact Specimen Local Crack-Plane Mesh Four-layer model: (0.6, 1, 1, 0.6 mm) Nodes: 14,406 Elements: 9,264 E08.07.07 # 5 One-Eighth of Middle-Crack Tension Specimen Four-layer model: (0.6, 1, 1, 0.6 mm) Nodes: 11,697 Elements: 7,488 Same crack-plane element size and mesh pattern as C(T) specimen E08.07.07 # 6 ASTM May 2015 3
Local Crack-Opening Displacements during Stable Tearing with Constant CTOA along Centerline at Maximum Load x/c f E08.07.07 # 7 Local Crack-Opening Displacements during Stable Tearing under Constant CTOA at Maximum Load x/c f E08.07.07 # 8 ASTM May 2015 4
Local Crack-Opening Displacements during Stable Tearing under Constant CTOA at Maximum Load C.T. Sun Purdue University Mild steel x/c f E08.07.07 # 9 Local Crack-Opening Displacements during Stable Tearing at Constant CTOA and a Stationary Crack at Maximum Load x/c f E08.07.07 # 10 ASTM May 2015 5
Calculated K Ie against Initial Crack-Length-to-Width Ratio for M(T) Specimens using FEA-CTOA Fracture Simulations ZIP3D: c = 7.6 deg. E08.07.07 # 11 Predicted K Ie against Crack-Length-to-Width Ratio for C(T) Specimens using FEA-CTOA w = 64 mm w = 71 mm ZIP3D: c = 7.6 deg. E08.07.07 # 12 ASTM May 2015 6
NOTCH-STRENGTH ANALYSIS AND FRACTURE MECHANICS E08.07.07 # 13 Stress Concentration Factor for an Elliptical Hole in an Infinite Plate Inglis (1913) e = S K T E08.07.07 # 14 ASTM May 2015 7
Modern Fracture Mechanics Paul Kuhn George Irwin Notch Strength Analysis Fracture Mechanics (Neuber ) (Griffith) E08.07.07 # 15 Elastic-Plastic Stress- and Strain-Concentration Factors using Neuber s Equation Neuber (1961): Hutchinson, Rice (1968) showed that the stress strain field for a crack in a non linear elastic material verified Neuber s equation Crews (1974) experimentally validated Neuber s equation for elliptical hole in finite plate under remote uniform stress E08.07.07 # 16 ASTM May 2015 8
Original Two-Parameter Fracture Criterion Inglis stress-concentration equation for elliptical hole, K T = 1 + 2 (c/) Neuber s equation: K K = K 2 T K F = K Ie / = 1 m (S n / u ) ( n u) for S n < ys ( ys /S n ) [1 m (S n / u )] for S n ys Constraint effects on net-section NOT considered! E08.07.07 # 17 Modified Two-Parameter Fracture Criterion Inglis stress-concentration equation for elliptical hole, K T = 1 + 2 (c/) Neuber s equation: K K = K 2 T K F = K Ie / = 1 m (S n /S u ) for S n < ys ( ys /S n ) [1 m (S n /S u )] for S n ys S u = u for M(T) and S u 1.61 u for C(T) E08.07.07 # 18 ASTM May 2015 9
Calculated K Ie against Crack-Length-to-Width Ratio for M(T) Specimens using FEA-CTOA and TPFC ZIP3D: c = 7.6 deg. TPFC: K F = 230 MPa-m 1/2 m = 0.9 E08.07.07 # 19 K Ie against Crack-Length-to-Width Ratio for C(T) Specimens E08.07.07 # 20 ASTM May 2015 10
Predicted K Ie against Crack-Length-to-Width Ratio for C(T) Specimens using TPFC with Plastic-Hinge Stress TPFC: K F = 230 MPa-m 1/2 m = 0.9 (S n > ys ) E08.07.07 # 21 Predicted K Ie against Crack-Length-to-Width Ratio for C(T) Specimens using TPFC (S u replaced with u ) E08.07.07 # 22 ASTM May 2015 11
Outline of Presentation Finite-element fracture simulations using ZIP3D and critical CTOA fracture criterion on 7249 aluminum m alloy Notch-Strength Analysis and Fracture Mechanics Comparisons with Two-Parameter Fracture Criterion Finite-element fracture simulations using ZIP2D (plane-strain core) and critical CTOA fracture criterion on 2219 aluminum alloy Comparisons with Two-Parameter Fracture Criterion Concluding remarks E08.07.07 # 23 Capabilities of ZIP2D Code Elastic or Elastic-Plastic Non-Linear FE codes Element types: - Constant-strain triangular (3-noded) element (Plane-stress, plane-strain or plane-strain core) Classical Plasticity Material Non-Linearity: - Prandl-Reuss-Drucker & Zienkiewicz - Elastic-perfectly plastic, bilinear, multi-linear or - Ramberg-Osgood g stress-strain curve Hardening: Isotropic or Kinematic Fatigue and Fracture: - Fracture parameters K and J - Stable crack growth using CTOA (or CTOD) - Cyclic crack growth and crack closure E08.07.07 # 24 ASTM May 2015 12
Crack Configurations Analyzed S S S M 2c i 2c i c i i c i i 2w 2w w w w w S S MS (a) Middle (a) tension (b) Single-edge (b) tension (c) Single-edge (c) bending E08.07.07 # 25 Plane-Strain Core in Plane-Stress Finite-Element Model S Plane Stress Plane strain Strain 2h c Finite-element codes: ZIP2D STAGS Crack Plane Stress Plastic zone FEA C.T. Sun (Purdue Univ.) S E08.07.07 # 26 ASTM May 2015 13
Failure Stress against Specimen Width on 2219-T87 E08.07.07 # 27 Typical Load-against-Crack-Extension using Critical CTOA Fracture Criterion E08.07.07 # 28 ASTM May 2015 14
Crack-Opening Displacements for Stably Tearing Crack x/c f E08.07.07 # 29 Crack-Opening Displacements for Stationary and Stably Tearing Crack x/c f E08.07.07 # 30 ASTM May 2015 15
Influence of Width and Crack Length on K Ie at Failure for 2219-T87 Aluminum Alloy E08.07.07 # 31 Two-Parameter Fracture Criterion Analysis on 2219-T87 Aluminum Alloy M(T) Specimens SS w = 610 mm w = 76 mm 2c i 2c i 2w 2w S (a) E08.07.07 # 32 ASTM May 2015 16
Elastic Stress-Intensity Factor at Failure for Wide Range of Middle-Crack Tension Specimens SS 2c i 2c i 2w 2w S (a) E08.07.07 # 33 Elastic Stress-Intensity Factor at Failure for Limited Range of Middle-Crack Tension Specimens SS 2c i 2c i 2w 2w S (a) E08.07.07 # 34 ASTM May 2015 17
Elastic Stress-Intensity Factor at Failure for Wide Range of Single-Edge-Crack Tension Specimens SS c ic i w w S (b) E08.07.07 # 35 Elastic Stress-Intensity Factor at Failure for Wide Range of Bend Specimens S M c ic i w w M S (c) E08.07.07 # 36 ASTM May 2015 18
Concluding Remarks 1. Finite-element analysis (FEA) fracture simulations using critical crack-tip-opening-angle (CTOA) fracture criterion were able to correlate and predict failures on M(T) and C(T) crack configurations made of 7249 and 2219 aluminum alloys. 2. FEA-CTOA fracture simulations were consistent with Two- Parameter Fracture Criterion (TPFC) characterization for M(T), SEC(T) and SEC(B) specimens for net-section stresses less than yield stress (S n < ys ). 3. TPFC failure analyses on tension and bend specimens were very good for large widths, but not small widths (S n > ys ). 4. More work required on bend-type specimens and accounting for constraint variations on net-section. E08.07.07 # 37 ASTM May 2015 19
Progress in Development of Proposed CTOA Test Method and Rotation Factor S. Xu, C.H.M. Simha, M. Gesing and W.R. Tyson ASTM May Committee Meeting May18 18, 2015 Anaheim, CA, USA
Outline Background of CTOA Progress made since November 2014 meeting Rotation factor (r p ) Discussion on r p correlation recommendation p and next steps
Theoretical Work on the Physical Significance ifi of the Determined CTOA CTOA has been used as a parameter for fracture propagation since Rice/Sorensen s original groundwork; the following references are examples. Rice, J. R., and Sorensen, E. P., "Continuing Crack Tip Deformation and Fracture for Plane Strain Crack Growth in Elastic Plastic Solids", J. Mech. Phys. Solids, 26, 1978, pp. 163 186. Rice, J.R., Drugan, W.J., and Sham, T.L., Elastic plastic Analysis of Growing Cracks, ASTM STP 700, ASTM, Philadelphia, PA, 1980, pp. 189 221. Newman, J.C. Jr., James, M.A., and Zerbst, U., A Review of the CTOA/CTOD Fracture Criterion, Eng. Fract. Mech., 70, 2003, pp. 371 385. Further progress requires treatment of propagation using micro mechanical models dl( (e.g., Xue Wierzbicki or Gurson models, dl etc.) as is bi being advanced dby FEA. The CTOA concept has been successful for the aerospace industry (aging aircraft) and has been developed to apply for gas pipeline fracture arrest.
Other Considerations of CTOA The relation to other measures of CTOA: CTOA is the angle formed dby the flanks of the propagating fracture, and this angle characterizes the propagation toughness the same way that the CTOD characterizes the initiation toughness. Application of CTOA in pipelines: One key issue in pipeline applications has been to devise a practical labscale test to measure it and the proposed test method is to address this. The CTOA approach is to enable prediction of the relation between propagation speed, pressure, and pipe properties (diameter, thickness, strength, density, ) by using CTOA as propagation criterion in an FEA model.
Development of CTOA based Fracture Arrest Methodology in the Pipeline Industry The first CTOA-based model with a two-specimen CTOA test method that is not suitable for modern high-strength steels: More recent CTOA-based model method (PICPRO TM ): The background of CTOA test method has been presented in Journal of Pipeline Engineering in 2013:
Modeling of CTOA Damage mechanics model has been applied to DWTT specimen successfully to load vs. deflection and deformed geometry (Simha, Xu and Tyson, Engineering Fracture Mechanics, 2014) Effect of T stress on CTOA usingcohesive zone modelling (Parmar, Wang, Tyson and Xu, PVP2015)
Progress Made Since November 2014 Committee Meeting Significant editorial modifications have been made to address comments from E08.07 members. A draft report on Inter laboratory Study to Establish Precision Statements for ASTM has been prepared. Rotation factor has been determined dusing FEA and the p test.
CTOA B/2 ( ) 18 16 14 12 10 8 6 4 2 0 Development of Precision and Bias Clauses Lab 1 Lab 2 Lab 3 Lab 4 Lab 5 Lab 7 Participant for the Proposed Test Table 4. Statistics of results from ILS on CTOA B/2 measurement. Repeatability Reproducibility Repeatability Reproducibility Parameter Average Standard Standard Limit Limit Deviation Deviation CTOA, 12.3 0.9 2.0 2.6 5.6 Precision Values of CTOA measured from an X70 pipe steel of thickness t = 12.7 mm reported in the framework of an interlaboratory study (ILS) using a draft recommended practice have been analyzed in accordance with Practice E691 in order to establish the precision of the test method. The terms repeatability limit and reproducibility limit are used as specified in Practice E177. The interlaboratory study involved five laboratories. Each laboratory provided between three and five CTOA test results. The results of the statistical analysis are summarized in Table 4. Note: The statistical analysis was done in collaboration with Dr. Enrico Lucon, National Institute for Standards and Technology (NIST), Boulder, CO (US).
Determination of Rotation Factor CTOA 2 tan 1 4r * S dlnp dy The plastic hinge model assumes that the two arms of a DWTT specimen rotate symmetrically about an axis of rotation located in the uncracked ligament. The ratio of the distance between the crack tip and the hinge line to the length of the remaining ligament is defined as the plastic rotation factor (r p ). The rotation factor can be obtained from experiments and FEA calculation from the location of the center of gravity or force balance. where: P is the load and y is the deflection from the tests S is the load span r* is the rotation factor 17.11 mm 8.9 89 mm (A tested DWTT sample) a 2 a 1 a rp a 1 2
Determination of Rotation Factor by FEA Approach Finite element analysis is performed using the modified Xue Wierzbicki damage mechanics model (C.H.M. Simha, et al., Eng. Fract. Mech., 2014). The CVN was adjusted by modifying the parameters which control the damage evolution function. Reference: C.H.M. Simha, S. Xu and W.R. Tyson, Non Local Phenomenological Damage Mechanics Based Modeling of the DWTT, Engineering Fracture Mechanics, Vol. 118, 2014, pp. 66 82.
Determination of Rotation Factor by FEA Results Twelve simulation cases were performed. Case Nominal Grade σy [MPa] B [mm] CVN [J] n rp 1 X52 386 13.7 63 0.136 0.55 2 X52 386 13.7 200 0.136 0.60 3 X65 485 13.7 98 0.146 0.57 4 X70 590 13.7 222 0.160 0.58 5 X100 818 13.7 259 0.072 0.56 6 X100 818 13.7 60 0.072 0.54 7 X65 485 20 98 0.146 0.54 8 X65 485 6 98 0.146 0.53 9 X100 818 20 259 0.072 0.57 10 X100 818 6 259 0.072 0.60 11 X52 386 13.7 48 0.136 0.55 12 X80 571 13.7 442 0.132 0.60 Charpy force vs. deflection for typical cases a 2 a 1 a rp a 1 2
A linear model assessment for r p was performed using the p value test (http://en.wikipedia.org/wiki/p value or Statistics for engineers and scientists by William Navidi, Chapter 6 ). The p value is defined as the probability under the assumption of a particular hypothesis of obtaining a result equal to or more extreme than what was actually observed. The smaller the p value, the larger the significance. If p value < 5%, then the variable influences r p Linear Relation P value CVN 0.012.405 0.59 0.65 CVN 0.005 0.007 0.002
The p value is based on rotation tti factors determined dt dexperimentally for a number of pipe steels tested under impact. Linear Relation P value CVN 0.101 0.957 0.713 0.899 CVN 0.025 0.050 0.033
r p as a function of CVN/(σ y B) r p 0.59 0.58 058 0.57 0.56 0.55 0.54 y = 0.5775x + 0.5473 R² = 0.5003 0.53 0.00 0.02 0.04 0.06 0.08 CVN/(σ y B) Fitting to experimental impact results CVN(σ y B) Fitting from Exp Experimental data Steel rp rp Impact C1 0.58 0.59 C2 0.58 0.57 C3 0.58 0.57 C4 0.57 0.56 C5 0.55 0.56 C6 0.54 0.55 X65 (CO2) 0.56 0.57 X70 (RR) 0.57 0.57 Slow rate C1 0.55 0.59 C2 0.57 0.57 C3 0.58 0.57 C4 0.57 0.56 C6 0.55 0.55 X65 (CO2) 0.57 0.57 FEA X52 0.55 0.55 X52 0.60 0.57 X65 0.57 0.56 X70 0.58 0.56 X100 0.56 0.56 X100 0.54 0.55 X65 0.54 0.55 X65 0.53 0.57 X100 0.57 0.56 X100 0.60 0.58 X80 0.60 0.56 X52 0.55 0.56 r p from fitting experiment data
r p as a function of CVN r p 0.60 0.59 0.58 0.57 0.56 0.54 y = 0.0001x + 0.5412 R² = 0.5963 CVN Fitting from Exp Experimental data Steel rp Impact C1 0.58 0.59 C2 0.58 0.57 C3 0.58 0.57 C4 0.57 0.56 C5 0.55 0.57 C6 054 0.54 055 0.55 X65 (CO2) 0.56 0.56 X70 (RR) 0.57 0.57 Slow rate C1 0.55 0.59 C2 0.57 0.57 C3 0.58 0.57 C4 057 056 C6 0.55 0.55 X65 (CO2) 0.57 0.56 FEA X52 0.55 0.55 X52 0.60 0.56 X65 0.57 0.55 X70 058 0.58 056 0.56 X100 0.56 0.57 X100 0.54 0.55 X65 0.54 0.55 X65 0.53 0.55 X100 0.57 0.57 X100 060 0.60 057 0.57 X80 0.60 0.59 X52 0.55 0.55 055 0.55 C4 0.57 0.56 0.53 0 100 200 300 400 500 CVN (J) Fitting to experimental impact results r p from fitting and experimental data
r p as a function of CVN/σ y r p 0.59 CVN/σ y Fitting from Exp Experimental data y = 0.0518x + 0.5438 0.58 R² = 0.559 p 0.57 0.56 0.55 0.54 0.53 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 CVN/ y (J/MPa) Fitting to experimental impact results Steel rp rp Impact C1 0.58 0.59 C2 0.58 0.57 C3 0.58 0.57 C4 0.57 0.56 C5 0.55 0.56 C6 0.54 0.55 X65 (CO2) 0.56 0.57 X70 (RR) 0.57 0.57 Slow rate C1 0.55 0.59 C2 0.57 0.57 C3 0.58 0.57 C4 0.57 0.56 C6 0.55 0.55 X65 (CO2) 0.57 0.57 FEA X52 0.55 0.55 X52 0.60 0.57 X65 0.57 0.55 X70 0.58 0.56 X100 0.56 0.56 X100 0.54 0.55 X65 0.54 0.55 X65 0.53 0.55 X100 0.57 0.56 X100 0.60 0.56 X80 0.60 0.56 X52 0.55 0.56 r p from fitting and experimental data
Recommendation and Discussions Recommendation of rotation factor (r p ): to be discussed in this meeting. Next steps: to be discussed in this meeting. Thanks and Questions
DC Potential Drop Development Task Group E08.07.09 Meeting of May 18 th, 2015 Anaheim, CA Enrico Lucon NIST, Boulder Colorado (USA)
Developments since Nov 2014 Draft 2 of Annex A18 (Guidelines for the Use of Electric Potential Difference Methods for the Determination of Crack Size) was discussed at the last Task Group meeting in New Orleans LA (November 10, 2014). Based on the discussion in New Orleans, Draft 3 was produced and circulated for comments to Task Group members in February 2015. Comments from only a couple of TG members were received, and Draft 4 was prepared in April 2015. An ASTM Collaboration Area was created in April 2015 and Draft 4 was uploaded. All Task Group registered members were invited to join the collaboration area (19 joined).
Main changes from Draft 2 to Draft 4 Fig. 18.1 modified to match the voltage probe positions shown in Fig. A18.2 for the C(T) specimen and to make the C(T) specimen more similar to E1820 Annex 2 geometries. A18.7.3 Removed option to attach current wires to gripping apparatus This can cause variability in contact resistance. A18.7.4 Removed sentence about location of current wires not being critical Calibration is influenced by wire location. Note A18.3 Added that example refers to 20 C measurements. Two new sections added: A18.9.4 Selection of Input Current Duty Cycle A18.9.5 Selection of Input Current Pulse Duration. Note A18.4 (new) Plasticity at pin holes can affect PD signal.
Main changes from Draft 2 to Draft 4 A18.6 (Gripping Considerations) Simplified following suggestions by K. Tarnovski. A18.12.2 added Insensitivity of crack size vs. EPD relationships to temperature, material and specimen configuration. A18.12.3 added Typical forms of analytical crack size vs. EPD relationships. A18.2.4 C(T) relationships are not applicable to DC(T), but no specific relationship for DC(T) is available. Annex will remain restricted to SE(B) and C(T) specimens.
Main changes from Draft 2 to Draft 4 Significant changes to Section A18.13 (Effects of Plasticity on Electric Potential Difference) Previous 5 % offset method removed by popular demand. Approach standardized in ISO 12135 added in A18.13.2, complemented by recent research by K. Tarnovski. Note A18.4 added Warning that onset of crack extension may correspond to very subtle slope changes for some materials. New A18.13.4 added Use of V 0 for calculating crack size or crack extension. Also described: establishment of linear calibration between a and V (also standardized in ISO 12135).