PSI - Issue 13

Johannes Tlatlik et al. / Procedia Structural Integrity 13 (2018) 243–248 Johannes Tlatlik, Dieter Siegele / Structural Integrity Procedia 00 (2018) 000 – 000

246

4

Upon increase in testing temperature a clear increase in the amount of detected cleavage fracture islands per specimen can be seen. On the other hand, a reduction of crack tip loading rate leads to an increase as well. Overall, there appears to be a more general dependence with the achieved fracture toughness K Jcd,1T , and global failure can be postponed due to local crack arrest up to 14 times. Worth emphasizing is also the fact that local crack arrest can also be very frequent at very low crack tip loading rates of ̇ ≈ 10 3 MPa√m/s (ca. 0.025 m/s impact velocity). Furthermore, the size of the cleavage fracture islands depends on testing conditions as well. The majority of arrested cracks stop propagating after about 0.03 to 0.04 mm leading to a diameter of about 0.06 to 0.08 mm. Arrested cracks of greater length are increasingly less likely, whereas higher testing temperatures clearly allow the material to arrest larger cracks. So in conclusion, the probability of local crack arrest increases with decreasing loading rate and increasing temperature. Noteworthy here, is that due to the adiabatic heating in the crack tip region local temperature can deviate strongly from the nominal testing temperature (see Tlatlik (2017b)). Also, a strong impact of the prevailing maximum principal stress σ I in the cleavage fracture zone is assumable. Higher crack tip loading rates lead to higher σ I -values which are assumed to be the driving force of a dynamically propagating cleavage crack. At similar temperatures such a crack is more improbable to be arrested compared to lower crack tip loading rates. This explains the decreasing amount of observed cleavage fracture islands as a result of higher crack tip loading rates shown in Figure 1 b). The SE(B)40-20 specimens were modelled in 3D. For reasons of numerical stability a crack front with a radius of 1 5 μm was used with the aid of fully -integrated 8-node volume elements with a linear displacement function. Displacement-controlled load of the striker was applied according to average experimental CMOD-time courses of the respective loading rates. The calculated dynamic crack tip loads K Jd (t) are in good agreement with the experimental observations Tlatlik (2017b). Anvil and striker were modelled as rigid-body cylinders, respecting compliances and assumed nearly friction- free (μ = 0.001). All calculations were conducted geometrically non-linear with consideration of large plastic deformations by using the ABAQUS implicit solver allowing heat generation and conduction. A parameter study regarding inertia effects in Tlatlik (2017b) justified the negligence of elastic wave propagation during testing. Temperature-dependent values for standard ferritic steel regarding thermal conductivity, heat capacity, thermal expansion, and density were incorporated. Elastic material properties were described by Hooke’s law with a temperature- dependent Young’s modulus, and the plastic behavior by the v. Mises flow model with isotropic hardening. Basic data regarding elastic-plastic material properties were obtained from high-speed tensile tests performed by Mayer (2015) and adjusted in Reichert et al. (2017b). Ductile crack growth was considered as well, in the sense that elements at the crack tip were deleted during the simulations according to the experimentally measured ductile crack lengths as a function of J -Integral. The J -Integral at the crack tip was calculated by ABAQUS contour integrals and weighted according to the respective element size along the crack tip, after which an effective J -Integral was obtained that represents the entire crack front, and used to calculate the relevant load K J , and then the size-corrected value of K J,1T according to the terms stated in ASTM E1921. The presented cleavage fracture model acc. to Hohe et al. (2010) was first used to calculate fracture probability under quasi-static conditions at -110, -90, -70 and -50 °C. The model parameters were determined by a least square error technique regarding the probability of failure P f and crack tip load K Jd,1T so that the error between numerical simulation and experimental results was minimized. An optimal parameter configuration of σ th = 1500 MPa, σ u = 2500 MPa, a = 1.2, and temperature dependent values of C ( T ) = 44000, 37000, 16900, 5800 (for increasing testing temperature) was determined for quasi-static conditions. Using these parameters, the cleavage fracture model is able to describe fracture behavior quite well for this material regarding various testing temperatures. Analogously, the model parameters for the dynamic testing conditions were obtained while all mentioned parameters remained constant with the exception of C ( T , ̇ ), which was postulated as additionally dependent on 5.2. Calculation of Fracture Probability 5. Numerical Simulations 5.1. Finite-Element-Model