TWI Industrial Member Report Summary 988/2011
By D Zhou
A tearing resistance curve, or R-curve, represents a material's resistance to progressive crack extension (this implies that a material's fracture toughness can change with crack extension). Hence, a tearing resistance curve is a plot of fracture toughness against crack extension (eg J vs ?a or CTOD vs ?a, where ?a is crack extension).
J-R curve testing procedures for high-constraint specimens have been well established in many standard codes such as BS 7448 (BSI, 1997) and ASTM E1820 (ASTM, 2008). These standards allow the choice of multiple or single-specimen techniques to determine a J-R curve. The multiple specimen technique requires testing several specimens to determine a single J-R curve for a specific material, which results in a high material and labour cost. In contrast, the single-specimen method requires in principle only one specimen to determine a full J-R curve for a given material provided that it has been firmly established that the material shows upper shelf behaviour.
The single-specimen technique relies on indirect methods for measuring the crack extension. The most common approach to determine the crack extension during the test is through either the unloading compliance or the electric potential drop method. However, these two methods require sophisticated equipment and testing techniques. In particular, they cannot be used under severe testing conditions, such as high loading rate.
An alternative method to update the crack extension in the single-specimen technique is the normalisation method. This method is different from the unloading compliance approach in that it does not require unloading during crack extension. In other words, the normalisation method requires only the initial and final crack lengths and the load-displacement curve. The crack extension is updated using mathematical fitting as suggested in the appendix of ASTM E1820. The main advantages of the single specimen normalisation method are the quick test turn around and cost-effectiveness, and it is therefore potentially suitable for routine testing.
It is known that J-R curves depend significantly on constraint levels at the crack tip, which vary according to specimen type, size and loading types (Figure 1). However, both multiple- and single- specimen techniques (irrespective of the unloading compliance or normalisation methods) are standardised for high-constraint specimens only. Methods for R-curve testing of low-constraint specimens have been under development for some time in a number of research centres around the world, but the standardisation of those methods is limited. For example, there are no standards for such tests in the UK. Generally there is insufficient clear guidance in national and international test standards on the testing of low-constraint specimens and the interpretation of test results. Traditionally, the multiple specimen method is used for non-standard specimens such as SENT (single edge notched tension) and centre-crack tension (CCT) specimens. Use of the single-specimen technique for generating the J-R curve using low-constraint specimens is rather limited.
R-curve generation by modelling is increasingly of interest to researchers due to the low cost and convenience. A constraint-based R-curve can be modelled analytically by mathematical fitting. The analytical method requires at least three R-curves at different constraint levels; these R-curves are then used to derive a generalised constraint-dependent R-curve using an appropriate constraint parameter.
Physically, ductile fracture involves the typical stages of nucleation, growth, and coalescence of voids in the micro-scale. In order to consider the effects of these voids on the stress-carrying capability of a mechanical continuum during simulation, damage mechanics models are widely used. Ductile damage models such as those of Rousselier (1987) and Gurson-Tvergaard-Needleman (GTN) which was developed by Tvergaard and Needleman (1984) have been widely used for predicting load-deformation and fracture resistance behaviour of specimens and components. One drawback of these models lies in their use of a characteristic finite element (FE) size in the fracture zone to simulate the crack initiation and crack growth process when employing the FE method. Moreover, an ordinary GTN model of porous metal plasticity requires nine parameters and this makes the calibration of parameters time-consuming.
The cohesive zone model provides an alternative approach to model the damage and failure of materials and structures. Cohesive zone models employ a material model which is represented by a traction-separation law describing the loss of the stiffness of the material as a function of the separation. One advantage of the cohesive zone model over the GTN model is that only two parameters are needed.
- Review R-curve testing methods and carry out fracture tests for low-constraint specimens.
- Derive constraint-dependent R-curve using constraint parameters.
- Develop a method for predicting the J-R curve using the cohesive zone model.