Elastic compliance of single-edge-notched tension SE(T) (or SENT) specimens

B. Tyson et alii, Frattura ed Integrità Strutturale, 30 (2014) 95-100; DOI: 10.3221/IGF-ESIS.30.13 Focussed on: Fracture and Structural Integrity related Issues Elastic compliance of single-edge-notched tension SE(T) (or SENT) specimens B. Tyson1 CanmetMATERIALS, Hamilton, ON, Canada P. Ding, X. Wang Carleton University, Ottawa, Canada , ABSTRACT. There has been a trend recently to use specimen geometries for toughness measurement that are more representative of actual flaw geometries in service. A prominent example is the use of single-edge-notched tension specimens for assessment of surface flaws in pipelines. To obtain a resistance (R) curve, i.e. J-integral or CTOD as a function of crack growth, it is necessary to monitor the crack size as a function of J or CTOD. To facilitate obtaining these data from a single specimen, the elastic CMOD unloading compliance C has been used in several testing programs to estimate crack size. C is a function of several variables in addition to crack size – notably, specimen constraint (plane stress or plane strain). In this paper, the dependence of C on these variables will be discussed. KEYWORDS. SENT; SE(T); Constraint; Compliance; R-curve. INTRODUCTION: SE(T) TESTING C haracterization of resistance to fracture of the materials used in construction of engineering structures such as pipelines is a vital step in design. Conventionally, this has been done by using a test that gives a conservative material property (the “fracture toughness”) that can be compared with the estimated maximum crack driving force of a plausible flaw in service, and ensuring that the material selected has adequate toughness to prevent fracture. This is a safe way to proceed, but because of the high degree of conservatism in some cases it can lead to uneconomic design. In particular, for thin-walled structures such as pipe, the lower degree of constraint experienced by surface flaws can enable the material to withstand much higher driving force than in a highly-constrained test specimen. The logical response to this is to reproduce the actual service geometry and loads as closely as possible in the toughness test set-up. The resistance displayed by the material in this arrangement may not be a lower bound for the material, i.e. it may be “geometry-dependent”, but it will be the appropriate toughness to use in assessing the defect tolerance of the structure being simulated. The procedure for engineering critical assessment of circumferential surface flaws (i.e. weld defects) in line pipe is a case in point. It is well known that the constraint for such flaws is substantially lower than the constraint in the standard threepoint-bend test geometry. To generate toughness measurements more representative of the service conditions, tests with 1 © Her Majesty the Queen in Right of Canada, as represented by the Minister of Natural Resources, 2014. 95 B. Tyson et alii, Frattura ed Integrità Strutturale, 30 (2014) 95-100; DOI: 10.3221/IGF-ESIS.30.13 specimens of the same thickness as the pipe, notched in the same orientation as the surface flaws being assessed and loaded in tension to simulate service loads, have been developed. Several variants of the test, using single-edge-notched specimens loaded in tension (SENT or SE(T)), are in existence. The first, RP-F108 published by Det Norske Veritas [1], uses multiple specimens. The RP-F108 specimens are of preferred cross-section 2BxB (thickness x width: the dimension B here refers to specimen width, which is the pipe wall thickness in this case; normally, B refers to the specimen thickness, but there is no confusion for BxB cross-section specimens which will be the focus of the remainder of this paper), and “daylight” (distance between grips) of H=10B (i.e. 10W), tested in tension. In the years since RP-F108 appeared, many papers dealing with SENT testing have been published as well as two test methods in draft standard form, i.e. CANMET’s recommended procedure [2] and ExxonMobil’s procedure for measurement of CTOD using SENT specimens [3]. The latter two tests report single-specimen methods relying on a crack-mouth-opening (CMOD) unloading compliance (UC) technique to monitor crack size during the test. The intent of the present report is to discuss details of the UC method. To estimate crack size using UC, a relationship between crack size and compliance is required. Estimation of this relationship is straightforward using standard linear-elastic finite element methods available in several software codes, and has been performed in many laboratories around the world. However, there are some subtleties in application of the results that should be recognized, in particular the relationship between plane strain and plane stress and which of these is the closest approximation to the actual test constraints. ESTIMATION OF CRACK SIZE - PLAIN STRESS/STRAIN T he most straightforward procedure to obtain stress and displacement using finite element analysis (FEA) is to use a two-dimensional (2D) plane strain model. Plane stress constraints are difficult to simulate, and resort is normally made to a “generalized plane stress” formulation for this case. The resulting compliance data can be expressed in terms of a parameter u (sometimes called the “normalized compliance”): u=1/(√(BCE´)+1) (1) where B=specimen width, C=CMOD compliance (displacement/load), and E´ is the “effective modulus”. For planestrain compliance calculations, the appropriate “effective modulus” is the “plane-strain modulus” E´=E/(1-ν2) where ν is Poisson’s ratio for the material. The actual specimen constraints are, of course, not plane strain but rather something between plane strain and plane stress (see, for example, [4]). To obtain the plane stress compliance from Eq. (1), the “plane stress modulus” E´=E should be used, where E is Young’s modulus for the material. In practice, the relationship between a/W and u is first found from plane-strain FEA calculations, and expressed in a convenient form, normally a polynomial for a/W as a function of u. Then, to estimate a/W from compliance, the value of u using the “effective modulus” appropriate to the constraint of the test specimen is calculated from the measured compliance. Then, a/W is calculated from the polynomial for a/W as a function of u. Polynomial expressions for a/W have been published in a number of papers. It has become conventional to use a “daylight” H between grips of 10W and fixed-grip (clamped) load application, and most use a BxB cross-section geometry; all of the results discussed here are for this condition. All previously published results are in essential agreement. According to Shen et al. [2], a/W = 2.044 - 15.732u + 73.238u2 – 182.898u3 + 175.653u4 + 60.930u5 – 113.997u6 – 113.031u7 + 8.548u8 + 142.840u9 (2) This expression is rather cumbersome, but since the equation is intended to be valid over the extended range of a/W between 0.05 and 0.95, to maintain accuracy (...truncated)