Identification of CTOA and fracture process parameters by drop weight test and finite element simulation
Introduction
Ductile crack propagation in metals is accompanied with an extended plastic zone ahead the crack tip, particularly when thickness is small compared to other dimensions. If the driving force does not decrease during crack propagation, the fracture can widely extend, as it can effectively happen in pressurized pipelines suffering longitudinal cracks. Such events are characterised by a high dynamics, so that the central difference scheme for finite element solution is well suited. In the field of the engineering structures here accounted, considering the wide plasticity induced during crack propagation, traditional crack models cannot be easily managed. Furthermore, traditional crack models, applied to finite elements, need a fine discretisation which, for central difference scheme, causes an unacceptable decrease of the computational time step [1]. The alternative can be found by using cohesive fracture models which, if well suited on material properties and geometry, allow the use of non-excessively refined meshes, thus keeping a sufficiently high value of the time step. This is a mandatory requirement for practical use of central difference integration scheme. This approach is followed in the pipe crack propagation code, jointly developed by the University of Rome “Tor Vergata” and the Centro Sviluppo Materiali S.p.A., where cohesive fracture zone modelling is made possible together with other peculiar facilities (fluid dynamic modelling of real gas expansion, backfill constraint effects, …) for the analysis of longitudinal cracks, running on pressurized buried pipes [2].
The cohesive zone model is one-dimensional, and finite element node release is carried out progressively; so that, the energy released during the steady propagation of a crack does not present discontinuities related to the mesh and keeps constant. As it is discussed within the paper, the use of the cohesive zone model requires the previous determination of two parameters: the critical crack tip opening angle (CTOAC) of the material [3], and the size of the cohesive zone involved in the local progressive softening.
According to several researchers [4], [5], [6], far from transitory conditions, CTOA assumes a constant value when stable propagation occurs; its value depends on material and geometry.
Therefore, stable growth is achieved only if the applied CTOA reaches the critical one. CTOA is, on the other side, unable to establish crack initiation conditions; other criteria must be invoked in this case. From a mathematical point of view, CTOA is the Lagrangian derivative of crack tip opening displacement. If CTOD is assumed to characterise the crack growth, CTOA is related to the changing rate of the crack speed. Cohesive models also allow the monitoring of the essential work of fracture within the cohesive zone (fracture process zone, FPZ). This is the energy requested only for the generation of new crack surfaces. This quantity, if reliably estimated, could be a new key for the evaluation of high ductile crack propagation [7], [8], [9], [10].
The aim of the present work is to describe the experimental set up and the numerical procedures that are required to tune the cohesive zone model for its use on engineering structures suffering long crack propagation. These conditions occur, as an example, in steel gas pipelines, when, due to incidental reasons (corrosion, impact with excavators, etc.), a wall thickness failure occurs and ductile fracture starts to propagate, driven by escaping gas force.
Section snippets
One-dimensional cohesive model
In the present paper a one-dimensional cohesive zone model for the simulation of the progressive formation of the crack flanks is discussed. The progressive nodal release technique here discussed provides a layer (cohesive zone), located behind a virtual crack tip, where the ability of the material to resist to the separation of the flanks is gradually reduced to zero. According to the modelling technique proposed, the CTOA is the geometric angle that the crack flanks form in correspondence of
First determination of CTOA parameter
Several approaches allow to determine the critical value of CTOA that is a characteristic of stationary crack propagation in a material (CTOAC) as many authors [4], [5], [6] have highlighted. Within the present paper, a particular method is explained, able to identify CTOAC on non-thin specimens, when optical methods lose efficiency, because of change in the emerging angle inside the bulk. This method is based on energetic considerations, by means of an approach that is called two specimen CTOA
Experimental–numerical combined computation of cohesive parameters
The cohesive zone model proposed cannot be applied by simple knowledge of critical CTOA. As previously described, the model needs the identification of two parameters. The first one is the critical CTOA, whose determination has been explained in Section 3.3. CTOAC determination is straightforward from experimental data. On the other hand, the size of FPZ Δ is derived comparing instrumented hammer history data with finite element results during a DWTT. At present this numerical–experimental
Numerical reliability of results
Finite element code PiCPRO is able to simulate ductile crack propagation in both specimens and large (i.e. long pipeline) structures. For the specific case of a DWT test, crack speed can be governed both with a kinematic equation (25) and with an actual comparison of a fracture mechanical parameter with its critical value, that establishes the propagation conditions (Free Propagation Algorithm––FPA). Applied CTOA, when compared time by time to critical CTOA, is an example of this second
Conclusions
In the paper it was shown that the use of a cohesive zone model for crack advance on ductile material can offer a favourable solution in engineering structures. Cohesive zone model requires the identification of two parameters: CTOA and Δ. The first one can be found by pure experimental evidences, while, at present, Δ assessment needs the coupled use of experimental data and finite element results from a DWT test. This is also the actual weakest point of the entire procedure. Δ is a quantity
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2020, Soil Dynamics and Earthquake EngineeringCrack tip opening angle during unstable ductile crack propagation of a high-pressure gas pipeline
2018, Engineering Fracture MechanicsCitation Excerpt :The drop weight tear test (DWTT) is a laboratory-scale test, and is the most fundamental test for evaluating a material’s resistance to ductile crack propagation in pipeline steels. Therefore, many studies evaluated the CTOA for pipeline steels [7,9–11,18,23,29,30,32,35]. The evaluation method on the CTOA has also been standardized as ASTM E3039 [36].
Simulation of ductile fracture in pipeline steels under varying constraint conditions using cohesive zone modeling
2018, International Journal of Pressure Vessels and PipingA model to evaluate unstable ductile crack arrestability of offshore pipeline
2017, Engineering Fracture MechanicsNumerical model for unstable ductile crack propagation and arrest in pipelines using finite difference method
2016, Engineering Fracture MechanicsCitation Excerpt :O’Donoghue et al. first proposed the finite element based model where gas flow, pipe deformation and crack propagation are coupled and the judgement for crack propagation/arrest is done by crack tip opening angle (CTOA) [9]. Subsequently, some FE based 3D models, where the coupling phenomenon among crack propagation, pipe deformation and gas decompression is incorporated, have been proposed [10–12]. However, these FE based model inevitably consumes long CPU time, which makes the calculation for full-scale burst tests impractical.