Crack tip opening displacement (CTOD) in single edge notched bend (SEN(B))

This thesis investigates the quantity Crack Tip Opening Displacement (CTOD) as a means to assess fracture toughness when measured in the Single Edge Notched Bend (SENB) specimen setup. A particular objective is to assess the effectiveness of the test when used for high strain-hardening materials (e.g. stainless steels). This has been an increasing concern as the current available methods were generally designed for lower strain hardening structural steel. Experimental work on CTOD tests included silicone casting of the crack, and constant displacement tests were also performed. The silicone castings enable physical measurement of the crack under an optical microscope. Results from a series of Finite Element (FE) models were validated from the experiments. δ5 surface measurements were obtained using Digital Image Correlation (DIC) as a courtesy of TWI, which were compared to surface CTOD measurements from the silicone castings. In addition to the experiments and Finite Element modelling, archived test data from TWI was processed, showing analytical differences between current Standard CTOD equations. CTOD calculations from BS 7448, ISO 12135, ASTM E1820 and WES 1108 were compared to the experimental and FE modelling results. For high strain hardening material, CTOD predicted by Standard equations (apart from those in BS 7448 and single point CTOD from ISO 12135) were lower than the values determined from silicone measurements and modelling. This potentially leads to over conservative values to be used in Engineering Critical Assessments (ECA) or material approval. Based on a series of different strain hardening property models, a relationship between strain hardening and the specimen rotational factor, rp was established. An improved equation for the calculation of CTOD is proposed, which gave good estimation of the experimental and Finite Element modelling results. The improved equation will be proposed for future amendments of the ISO 12135 standard. The results of this research enable the accurate fracture characterisation of a range of engineering alloys, with both low and high strain hardening behaviour in both the brittle and ductile fracture regime. WeeLiam Khor Crack tip opening displacement (CTOD) in Single Edge Notched Bend (SEN(B)) 4 Introduction Many factors contribute to the failure of an engineering component, i.e. flaw or inclusion in material, cyclic fatigue loading and residual stresses in the material. One of the most notable failure cases in history is the brittle fracture of Liberty Ships in 1940’s, where 1031 of 2078 ships experienced brittle related damage (Kobayashi & Onoue 1943). The lack of understanding in fracture at the time did not recognize material strength at low temperature and the effects due to weldments, which led to an expensive lesson in fracture. This incident led to more research in fracture mechanics, with two notable researches by Rice (1968) and Wells (1961). Fracture mechanics is a study of the material’s fracture resistivity, consisting two main parts: linear elastic fracture mechanics (LEFM) and elastic plastic fracture mechanics (EPFM). Linear elastic fracture mechanics describes the material’s fracture resistance within the elastic yielding region, mainly represented by stress intensity factor, K; the elastic plastic fracture mechanics considers post yielding where the crack deforms plastically, represented by the J-integral and crack tip opening displacement, CTOD. Experimentally, the fracture parameters K, J and CTOD are assessed through fracture toughness tests, where specimens are extracted from the actual structures and tested in a laboratory environment. Fracture toughness is typically used in Engineering Critical Assessments (ECA), where fracture mechanics theories are applied to evaluate the fitness of a structure for operation purposes. The tests are conducted in a controlled lab environment, where load and displacement feedback are used to infer the equivalent fracture toughness value. Normally, a fatigue crack is induced onto the specimen to represent the crack in a real operating environment. There are numerous different setup for fracture toughness testing, e.g. compact tension (C(T)), single edge notched bend (SEN(B)) and single edge notched tension (SEN(T)). The BS 7448-1 and ASTM E1820 are two of the most popular standards specifying methods of estimating fracture toughness, including CTOD. However, the equations do not agree with each other due to the different assumptions adapted for the formulation of the equations. This issue is known and thus researchers at the Japanese Welding Engineering Society, JWES proposed a new CTOD equation with the intention of estimating CTOD accurately. A series of fracture toughness tests were designed to validate the CTOD estimations using three materials with different strain hardening properties. To obtain a physical representative of CTOD, the crack in the specimens were casted using silicone compound, which gives a physical negative of the crack. The physical CTOD can be measured from the crack replica by using an optical microscope. The CTOD measured on the crack replica is considered the actual CTOD and was WeeLiam Khor Crack tip opening displacement (CTOD) in Single Edge Notched Bend (SEN(B)) 5 used as the baseline comparison against other methods. In addition to the experiments, finite element models were used to predict CTOD based on the material used in the experiments. Chapter 5.1 gives an analytical comparison between the different CTOD equations. Based on the resources available at TWI, data from 137 parent material SEN(B) tests were calculated using the CTOD equations from BS, ASTM and JWES. JWES overestimate BS for low strain hardening materials but underestimate higher strain hardening materials, whereas the ASTM consistently underestimate BS. Comparing the elastic and plastic CTOD, for low CTOD values, the elastic component of CTOD is dominant, and vice versa for high CTOD values. Chapter 6.1 describes the variation of CTOD across the specimen thickness in 20mm thick austenitic stainless steel. It was well known that fracture toughness varies across the crack front, but the standards did not explicitly specify the location for the assessment of CTOD. Experimentally, CTOD is affected by the curved crack front due to fatigue pre-cracking. An alternative definition of CTOD based on surface measurements, δ5 was extracted from seven specimens, compared to CTOD measured from the middle of the silicone replica. Additionally, CTOD was extracted from a straight crack front FE model to show the effect of crack front curvature. In Chapter 7.1, the accuracy of the CTOD equations are validated based on CTOD measured from the middle of the crack. The FE models representing the test specimens managed to give good estimation of CTOD. Comparing the CTOD based on the equations to the silicone replica and FE measurements, it was found that the equations generally underestimate CTOD, apart from the BS equation for higher strain hardening properties. The ASTM equation was seen to give lower estimation of CTOD regardless of the material strain hardening. The JWES equation seemed to give a good compromise between underestimation and accuracy for all strain hardening. Chapter 8.1 shows the effect of strain hardening on the CTOD tearing resistance curve, also described as the CTOD R-curve. The ISO, ASTM and BS equations were based on different assumptions and employed different crack correction factors for CTOD. Measurements from the silicone replica show that the material’s resistance to tearing increase with strain hardening property. Similar to that observed in Chapter 7.1, the BS equation overestimate the high strain hardening R-curve, and ASTM underestimate all R-curves. Despite not designed for R-curves, the JWES equation estimated the R-curves with adequate accuracy. The role of the rotational factor, rp in the determination of CTOD is described in Chapter 9.1. rp was extracted from both experiment and FE models shows that rp is not constant as assumed by BS and JWES. Including the effects of strain hardening in rp, rp increases with reducing strain hardening. The constant rp used by BS and JWES falls within the range of the rp corrected for strain WeeLiam Khor Crack tip opening displacement (CTOD) in Single Edge Notched Bend (SEN(B)) 6 hardening. The corrected rp estimated the silicone replica CTOD accurately despite some minor overestimation. Chapter 10.1 provides a discussion for the overall work. The implication of the different definition of CTOD and its effect on a propagating crack is explained. The necessity of the crack correction factor for R-curves is discussed. The chapter also explains the validity of the similar triangles concept and strain hardening correction for CTOD. WeeLiam Khor Crack tip opening displacement (CTOD) in Single Edge Notched Bend (SEN(B)) 7