Issue 30

B. Tyson et alii, Frattura ed Integrità Strutturale, 30 (2014) 95-100; DOI: 10.3221/IGF-ESIS.30.13 96 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. E STIMATION OF CRACK SIZE - PLAIN STRESS / STRAIN 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 plane- strain compliance calculations, the appropriate “effective modulus” is the “plane-strain modulus” E´=E/(1-ν 2 ) 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 + 73.238u 2 – 182.898u 3 + 175.653u 4 + 60.930u 5 – 113.997u 6 – 113.031u 7 + 8.548u 8 + 142.840u 9 (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 it was found necessary to include ten terms in the polynomial. Another polynomial was published earlier by Cravero and Ruggieri [5]: a/W = 1.6485 - 9.1005u + 33.025u 2 - 78.467u 3 + 97.344u 4 - 47.227u 5 (3) This equation contains only six terms, as it is valid only over the range 0.1≤a/W≤0.7. This is the relevant range for practical testing, and in that range it agrees well with Eq. (2). For purposes of the test standard then, Eq. (3) is adequate. Fig. 1 shows a comparison of Cravero’s Eq. (3) with Shen’s FEA data [2] and with data calculated in the present study. Note that Cravero’s equation (shown as a solid curve in Fig. 1) provides an excellent fit to Shen’s and the present results over the range 0.1≤a/W≤0.7, even up to a/W=0.8. There is a slight discrepancy for a/W=0.05 and a/W=0.9 and 0.95; however, these values of a/W are outside of the range expected to be used in practical tests. The conclusion is that Cravero’s equation is suitable for estimating crack size from CMOD compliance over the range 0.1≤a/W≤0.8. T