Mezzo-scopic Analysis of Fracture Toughness in Steels

Materials Research, Vol. 5, No. 2, 2002Vol. 5, No. 2, 85-93, 2002. Mezzo-scopic Analysis of Fracture Toughness in Steels © 2002 85 Mezzo-scopic Analysis of Fracture Toughness in Steels Takashi Miyata*, Tetsuya Tagawa Dept. of Materials Science & Engineering, Nagoya University, Nagoya 464-8603, Japan Received: August 28, 2001; Revised: December 29, 2001 The cleavage fracture toughness of steels was mezzo-scopically analyzed on the basis of the statistical local fracture criterion approach. The statistical stress criterion at the crack tip region suggests that the cleavage fracture toughness in steels can be described as a function of the yield stress, the cleavage fracture stress, and other mechanical properties of the materials. Formulation of the cleavage fracture toughness was first examined through an investigation on correlation between the cleavage toughness and the cleavage fracture stress obtained in notched round bar specimens in accordance with the theoretical prediction. Then, the scatter of the toughness, specimen thickness effect on the toughness, deterioration of the toughness due to cold working and irradiation, and improvement of the toughness caused by the Ni addition, were analyzed through the formulation of the toughness. Keywords: cleavage fracture toughness, local criterion approach, weibull stress, formulation of toughness, thickness effect, deterioration of toughness, steels 1. Introduction It is generally accepted that the transgranular cleavage fracture of steels in the transition temperature range is governed by the propagation of micro-crack nucleated at carbide particles, non-metallic inclusions and martensitic islands1-4. McMahon and Cohen1 had first demonstrated that the cracking of carbide particles at ferrite grain boundaries represents a primary cleavage fracture mechanism in steels. Many authors demonstrated up to the present that brittle cleavage fracture in steels initiates at some particles that are more harder and brittle than the surrounding ferrite matrix2-8. The cleavage fracture is promoted by factors that produce locally elevated tensile stress, since tensile stress governs the propagation of a micro-crack as a Griffith crack2,5-7. The cleavage crack once initiated can propagate with low energy dispersion and results unstable propagation. It implies that the fracture obeys the Weakest Link Analogy and statistical distribution of the critical fracture stress shows the Weibull distribution. Formulation of the Weibull stress criterion to describe the cleavage fracture of steels was first performed by Beremin9 and Mudry10. Incorporation of local criteria to analytical or numerical solutions for stress distribution at the crack tip derives an expression of fracture toughness in terms of flow and fracture properties of materials as is representatively shown in RKR model11. Statistical modeling for fracture proposed by Beremin gives more rational expression of the cleavage frac*e-mail: Trabalho apresentado no IV Coloquio Latinoamericano de Fractura y Fatiga ture toughness because the physical nature of the cleavage fracture is explicitly taken into account. The cleavage fracture toughness of steels is quite sensitive to metallurgical factors, and it strongly depends on temperature, strain rate and constraint due to variation in the specimen thickness, in the notch depth and in the scale of yielding at the crack tip12,13. Degradation in the toughness due to pre-straining, irradiation and strain aging, or so on, has been often reported. However, the factors that deteriorate the toughness have been individually, experimentally discussed till the moment. The dislocation theory and other microscopic approach may significantly contribute for analysis on the fracture and toughness of steels, while they give little quantitative information on mechanical factors responsible to the toughness. On the other hand, the mezzoscopic description or formulation of the toughness can be expected to give more comprehensive, more quantitative understanding of all subjects responsible to the toughness, and it may lead to the development of improvement of the toughness. Statistical model9 was successfully applied to analyze scatter of toughness14, increase of the toughness caused by the loss of constraint due to shallow notch15, and applied for qualification of the toughness16. In the present work, simplification of the statistical model is first performed to describe the cleavage toughness of various type of steels involving a mild steel and a low alloy steel. Theoretical de- 86 Miyata et al. scription of the toughness is experimentally confirmed through a correlation between the cleavage fracture toughness obtained in toughness test and the yield/cleavage fracture strength obtained in round bar tensile test. Then, the effects of various mechanical and metallurgical factors on the toughness are discussed on the basis of the comprehensive formulation of the toughness. The experimental results including those reported already elsewhere are analyzed. 2. Statistical Local Fracture Criterion and Description of Fracture Toughness According to the 2 parameter Weibull statistics, probability of failure for a certain volume of material, V subjected to gradient tensile stress σi is assumed to be m   σ  m   σ  dV  P = 1 − exp  − ∫ V  i  = 1 − exp  w     σ 0  V0    σ 0   (1) where, Vo is the statistical unit volume, m and σo are the shape parameter and the scale parameter of the Weibull cleavage fracture stress, respectively9. The Weibull stress is denoted as σω. Equation (1) can be applied to the fracture toughness specimen. With the assumption that the stress singularity at the crack tip is given in terms of normalized coordinate (r/J, r/K2) such as the HRR solution, the integral term in Eq. (1) is deduced to 4  K  σm m m ∫ V Vi0 dV =σ w = B  σ ys  σ ys F(n,m,V0) (2) Materials Research and the scatter of the toughness18. Instead of the Weibull cleavage fracture stress, the fracture stress defined in deterministic terms has been adopted in the present work to confirm the description of the fracture toughness by the local criterion approach, because it needs a great number of specimens to obtain the statistical Weibull parameters. In order to investigate the correlation between the fracture toughness and the cleavage fracture stress, more than 50 types low carbon structural steels including from a mild steel to a low alloy high strength steel with a yield strength of 250 MPa to 1,100 MPa, are tested. Cleavage fracture stress, σc is defined as the local maximum principle stress at the cleavage fracture initiation in round bar tensile specimens with 1mm radius circumferential notch as shown in Fig.1. Tensile tests were performed at the liquid nitrogen temperature and the critical stresses were calculated by the axisymmetric finite element analysis using the constitutive equation for each material. For several materials the (...truncated)