Experimental Estimation of J-R Curves from Load-CMOD Record for SE(B) Specimens

Abstract

Fracture resistance of ductile materials is often characterized by a J-R curve, and measured using the fracture toughness testing standard ASTM E1820 (Standard Test Method for Measurement of Fracture Toughness). The recommended elastic unloading compliance method or resistance curve test method requires simultaneous measurements of applied load (P), load-line displacement (LLD), and crack-mouth opening displacement (CMOD) from a single test for the single-edge notched bend [SE(B)] specimen. The P-CMOD record is used to determine crack extension, and the P-LLD record in conjunction with the crack extension is used to calculate the J-integral. However, it is well known that while highly accurate CMOD measurements can be made, the measurement of LLD is less accurate and more difficult because of transducer mounting difficulties, specimen load point indentions and load train deflections, or a combination thereof. Extensive finite element analyses showed that the LLD-based J equation may give inaccurate results for a shallow-cracked SE(B) specimen because its geometry factor η may depend on the strain hardening exponent. In contrast for the same geometry, the CMOD-based η factor is insensitive to the hardening exponent, and thus a CMOD-based J equation could be more accurate to be used in the determination of J-R curves. Based on the energy principle, this paper proposes a CMOD-based J equation for a growing crack using an incremental function similar to the present ASTM E1820-06 formulation that is applicable to the J calculations for a J-R curve testing. The proposed CMOD-based J formulation contains two geometry factors, i.e., CMOD-based η and γ, and can consider the crack growth correction. The solutions of four geometry factors are presented for the SE(B) specimens with a wide range of crack length. The proposed formulation is then applied to determine J-R curves for HY80 steel using the load-CMOD record for SE(B) specimens, and the results are compared with those using the traditional LLD-based formulation. The comparison shows close agreement between these two formulations. It is recommended that the proposed formulation be used in ASTM E1820 to determine more accurate J-R curves and reduce test costs as well.

Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization

“…However, the crack growth correction is indirect and complicated, with multiple analysis steps involved. Recently, Zhu et al [140] at Battelle Memorial Institute and at the US Naval Academy obtained a functional relationship between LLD and CMOD, and developed a long overdue CMOD method for the direct evaluation of crack growth corrected J-R curves. Based on the deformation theory of plasticity and following the ideas of Ernst et al [125], Zhu et al [140] obtained a CMOD-based incremental J-integral equation in a form similar to Eq.…”

“…These geometry factors can be determined using the accurate finite element analysis. For three-point bend SE(B) specimens, Zhu et al [140] proposed the following expressions for the two geometry factors: …”

Investigation of plastic eta factors for clamped SE(T) specimens based on three-dimensional finite element analyses

“…(7)-(9) for the PS specimens with a/W P 0.4, but are smaller than those given by Eqs. For a propagating crack, another geometry factor, c pl , is needed to make the crack growth correction in the eta factorbased evaluation of J [1,12,38]. Given Eq.…”

“…(16) and (17) respectively, J g values estimated through the use of Eqs. (1)-(4), (12), (16) and (17) were compared with the corresponding J ave values obtained from FEA. For comparisons, g LLD pl and g CMOD pl evaluated from Eqs.…”

“…The evaluation of g pl for the SE(B) and C(T) specimens based on two-dimensional (2D) and threedimensional (3D) FEA has been well reported in the literature (e.g. [5,7,8,[10][11][12]). …”