Cleavage Toughness Research Articles

Cutting soft matter: scaling relations controlled by toughness, friction, and wear.

Cutting mechanics of soft solids is gaining rapid attention thanks to its promising benefits in material characterization and other applications. However, a full understanding of the physical phenomena is still missing, and several questions remain outstanding. E.g.: How can we directly and reliably measure toughness from cutting experiments? What is the role of blade sharpness? In this paper, we explore the simple problem of wire cutting, where blade sharpness is only defined by the wire radius. Through finite element analysis, we obtain a simple scaling relation between the wire radius and the steady-state cutting force per unit sample thickness. The cutting force is independent of the wire radius if the latter is below a transition length, while larger radii produce a linear force-radius correlation. The minimum cutting force, for small radii, is given by cleavage toughness, i.e., the surface energy required to break covalent bonds in the crack plane. The force-radius slope is instead given by the wear shear strength in the material. Via cutting experiments on polyacrylamide gels, we find that the magnitude of shear strength is close to the work of fracture of the material, i.e., the critical strain energy density required to break a pristine sample in uniaxial tension. The work of fracture characterizes the toughening contribution from the fracture process zone (FPZ), which adds to cleavage toughness. Our study provides two important messages, that answer the above questions: toughness can be estimated from wire-cutting experiments from the intercept of the force-radius linear correlation, as previously explored. However, as we discovered, this only estimates cleavage toughness. Additionally, the force-radius slope is correlated with the work of fracture, giving an estimation of the dissipative contributions from the FPZ.

Microstructure-based cleavage modelling to study grain size refinement and simulated heat affected zones of S690 high strength steel

Study of the cleavage behavior of heat treated S690 steel by a microstructure-based approach combined with finite element analysis is present in this paper. Cleavage simulations of steels subjected to heat treatments that cause grain refinement or simulate heat affected zones are performed, and are compared with experiments. It is found that the experimental improvement of toughness from grain refinement is 80% of what would be expected based on the model. The 20% difference is due to the lower number fraction of high-angle misorientation boundaries. It is also found that the resistance to micro-crack propagation is more effective in heat affected zones, which can be explained by the residual compressive stress in martensite-austenite constituents. This research assesses the balance between microstructural parameters for controlling cleavage toughness.

A novel particle failure criterion for cleavage fracture modelling allowing measured brittle particle distributions

Most of the existing local approaches for cleavage fracture derive from the assumptions that global failure is a weakest-link event and that only the tail of the size distribution of micro-crack initiating features is significant. This appears to be sufficient in predicting lower shelf toughness under high constraint conditions, but may fail when attempting to predict toughness in the transition region or for low constraint conditions when using the same parameters. While coupled ductile damage models with Beremin-like failure probability could be useful in the transition region, uncoupled models with “a posteriori” probability calculations are advantageous to the engineering community. Cleavage toughness predictions in the transition regime, which can be extended to low constraint conditions, are here made with improved criterion for particle failure and experimentally based size distribution of initiators for specific RPV steel. The model is shown to predict experimentally measured locations of cleavage initiators. Further, the model predicts the fracture toughness in a large part of the transition region and accurately predicts the measured shift with irradiation, although further works is required to improve the model’s predictions at higher levels of fracture toughness and for low constraint conditions, which are expected to be achieved by a better accounting for plasticity. All results are obtained without changes in model parameters. This suggests that the model can be used as a tool for analysing toughness changes due to constraint and temperature driven plasticity changes.

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

The present paper gives a technical review of fracture toughness testing, evaluation and standardization for metallic materials in terms of the linear elastic fracture mechanics as well as the elastic–plastic fracture mechanics. This includes the early investigations and recent advances of fracture toughness test methods and practices developed by American Society for Testing and Materials (ASTM). The review describes the most important fracture mechanics parameters: the elastic energy release rate G, the stress intensity factor K, the J-integral, the crack-tip opening displacement (CTOD) and the crack-tip opening angle (CTOA) from the basic concept, definition, to experimental estimation, test methods and ASTM standardizing practices. Attention is paid to guidelines on how to choose an appropriate fracture parameter to characterize fracture toughness for the material of interest, and how to measure the fracture toughness value defined either at a critical point or in a resistance curve format using laboratory specimens. The relevant ASTM fracture toughness test standards considered in this paper are E399 for KIc testing, E561 for K–R curve testing, E813 for JIc testing, E1152 for J–R curve testing, E1737 for JIc and J–R curve testing, E1290 for CTOD (δ) testing, a combined common test standard E1820 for measuring the three parameters of K, J and δ, E1921 for the transition reference temperature T0 testing and the master curve of cleavage toughness KJc testing, and E2472 for CTOA testing. The effects of loading rate, temperature and crack-tip constraint on fracture toughness as well as fracture instability analysis are also reviewed.

A local approach model for cleavage fracture and crack extension direction of functionally graded materials

A local approach model has been developed for structural assessment of functionally graded materials in which the yield strength and the fracture toughness vary spatially. While the yield strength of the material at any point is taken to be deterministic, the local cleavage toughness is statistically distributed following a two-parameter Weibull model. The model is intended to determine the crack extension direction and failure probabilities of cleavage failure for a stationary pre-crack in a functionally graded material. The effect of independent variation in yield strength and toughness is discussed as a precursor to validating the model using a temperature gradient problem in which the yield strength and toughness are coupled through the temperature. The model is shown to closely reproduce experimental observations from cleavage fracture tests on mild steel subject to a controlled temperature gradient normal to the crack.

Fracture toughness characterisation in the ductile-to-brittle transition and upper shelf regimes using pre-cracked Charpy single-edge bend specimens

Fracture toughness data of pre-cracked Charpy single-edge bend, SE(B), specimens are compared with those of standard compact, C(T), specimens in the upper shelf and ductile-to-brittle transition regimes. Charpy sized SE(B) specimens provide ductile fracture toughness data, which are compatible with those of standard C(T) specimens. Statistical methods such as the exponential curve fitting method (ECF), the engineering lower bound toughness method (ELB), and the Master Curve method (MC) are used to provide meaningful lower bound cleavage fracture toughness estimates from the toughness scatter of the Charpy sized SE(B) specimens in the ductile-to-brittle transition regime. In this regime, according to the ELB and MC methods, SE(B) specimens provide cleavage toughness data, which tend to be non-conservative compared to those of standard C(T) specimens. However, analyses based on the exponential curve fitting method show good agreement between the fracture toughness estimates for the C(T) and Charpy size SE(B) specimens. At the lower bound toughness level (5% cleavage failure probability), corresponding to J=100 N/mm, the ductile-to-brittle transition curves of SE(B) specimens are reduced by 5–8 °C compared to those of standard C(T) specimens according to the MC-method. A constraint correction function for SE(B) specimens is presented that can be used to make cleavage toughness data of SE(B) specimens compatible with those of standard C(T) specimens.

The effects of warm pre-stressing on cleavage fracture. Part 1: evaluation of experiments

An experimental programme has been performed to characterise the mechanical parameters and the fracture response of two steels, BS1501 and A533B. These are widely used in pressure vessel technology. The role of load history on improvements in cleavage fracture toughness has been investigated. Scatter within experimental cleavage toughness data has been described by using the model proposed by Wallin [Defect Assessment in Components, Fundamentals and Applications, ESIS/EGF 9, Mechanical Engineering Publications, London, 1991, p. 415] and combined with Chell [Int. J. Fract. 17 (1981) 61] model for warm pre-stressing (WPS) effect. The influence of parameters such as repeated cyclic pre-loading, sub-critical crack growth and specimen size on the WPS effect has also been noted. Finally the importance of the role of crack tip blunting and near tip residual stress field in describing the effect is discussed.

Mezzo-scopic Analysis of Fracture Toughness in Steels

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.

The lower bound toughness procedure applied to the Euro fracture toughness dataset

The validity of a statistical method for estimating an engineering lower bound fracture toughness in the ductile-to-brittle transition region is investigated using the Euro fracture toughness dataset generated in the European SM&T Project “Fracture Toughness of Steel in the Ductile-to-Brittle Transition Regime”. The lower bound method is based on the empirical evidence that, in the low probability regime, the cumulative failure probability function tends to be a straight line rather than a curve as is the case for Weibull distributions. The investigation demonstrates that the engineering lower bound toughness values as predicted by the method are related to a cumulative cleavage failure probability lower than 2.5%. Such bound predictions can be achieved on the basis of a small number of cleavage toughness values measured at the temperature of interest. The results confirm the validity of the method.

Key features arising from structural analysis of the NESC-1 PTS benchmark experiment

Interpreting the results of the NESC spinning cylinder test represents a significant challenge for structural integrity specialists. The test was conceived to provide data on the behaviour of underclad defects and a large, through-clad defect under simulated PTS loading conditions. It contained the following structural features, the understanding of which is essential to obtaining a full interpretation of the test results: • cladding effects; • residual stresses; • constraint effect; • effective crack front width; • warm prestressing effect. The paper presents the results of the NESC-1 test with particular reference to the essential features listed above, and their relative importance. The paper notes that the most significant uncertainty factor that influenced the integrity assessment of the test is the variability of material toughness. This is in relation to both intrinsic variability (scatter) and that of the near-surface (clad/HAZ/base metal) region. There is some evidence to suggest that a loss of constraint influenced the near-surface behaviour of the largest underclad defect and the through-clad defect. However, the higher toughness of the HAZ, reduced crack front width (relative to that of a 25 mm CT specimen) and cladding effects are significant factors, too. The paper concludes by pointing out the need to provide (through continued international collaboration) validated procedures for relating fracture test data on specific specimen geometries to local constraint parameters estimated from 3D finite element simulations. Here, it is apparent that significant progress is to be gained from a formal unification of local approach methodology, the master curve description of cleavage toughness and ‘classical’ constraint-based fracture assessment methods.

Confocal microscopy–fracture reconstruction and finite element modeling characterization of local cleavage toughness in a ferritic/martensitic steel in subsized Charpy V-notch impact tests

The confocal microscopy (CM)–fracture reconstruction (FR) method, coupled with scanning electron microscopy (SEM) fractography, was used to measure the critical notch deformation conditions at cleavage initiation for two subsized Charpy V-notch (CVN) specimen geometries of Japan ferritic/martensitic steel (JFMS). A new method was developed to permit FR of notched specimens. Three-dimensional finite element analysis (FEA) simulations of the notch and specimen deformation were used to estimate values of critical micro-cleavage fracture stress, σ ∗ , and critical stressed area, A ∗ . Since σ ∗–A ∗ is independent of size and geometry, it provides a fundamental local measure of cleavage toughness.

A cleavage toughness master curve model

Development of fusion power will require a fracture toughness database, derived largely from small specimen tests, closely integrated with methods to assess first wall and blanket structural integrities. A master curve-shift (MC–ΔT) method has been proposed as an engineering expedient to treat the effects of structural geometry, irradiation, loading rates and safety margins. However, a number of issues related to the MC–ΔT method remain to be resolved, including the universality of MC shapes. A new micromechanical model of fracture toughness in the cleavage transition regime is proposed that combines analytical representations of finite element analysis simulations of crack-tip stress fields with a local critical stress-critical stressed area (σ∗–A∗) fracture criterion. This model, has been successful in predicting geometry effects, as well as high loading rate and irradiation hardening-induced Charpy shifts. By incorporating a modest temperature dependence in σ∗(T), an inconsistency between model predictions and an observed universal-type MC shape is resolved.

Fracture toughness of some high density PM steels

Tensile strengths, impact energies, and fracture toughness data are presented for pure Fe–0·5C, Astaloy A with 0·2 and 0·6%C, and for Distaloy AB–0·6%C at relative densities of about 0·9, achieved by conventional pressing and sintering, and at close to 1·0, achieved by powder forging. At low relative density, properties are controlled by sizes of sinter necks; it is postulated that toughness scales as (x/a)4, x/a being the ratio of neck diameter to particle diameter. At high relative density, microvoid coalescence and good toughness is observed for low strength micro-structures whereas cleavage and poor toughness is a concomitant of high strength.

Effects of crack size and weld metal mismatch on the has cleavage toughness of wide plates

The heat affect zone (HAZ) is in many cases considered to be the most critical part of a weldment. In this paper, the effect of crack size and weld metal mismatch on the HAZ cleavage toughness of wide plate specimens with X-groove has been investigated by the J- Q- M theories and a simple micromechanism for cleavage fracture. Two crack sizes have been studied ( a w = 0.1 and 0.3). In the analyses, the HAZ yield strength is assumed to be higher than the base metal. For each crack size, weld metal local overmatch and local evenmatch with respect to the HAZ are considered. For a given global strain, the results indicate that weld metal overmatch and evenmatch yield the same crack tip loading in terms of J-integral for a w = 0.3 . For a w = 0.1 , overmatch gives lower crack tip loading than evenmatch. For a given crack tip loading, weld metal local evenmatch in general results in less effective crack tip loading than the overmatch. Overmatch is detrimental to HAZ toughness, but this detrimental effect becomes less significant when the crack size decreases.

Cleavage and Static Toughness

Abstract The cleavage of adhesive joints allows the experimental study of the process of fracture in the low speed range. The value of the fracture energy deduced from the fracture length is the static toughness of the adhesive. This value, which determines the endurance limit of the joint, is much larger than can be explained by the current theories. It depends on the surface treatment of the substrate and results from the damage of the adhesive bonds. To take into account these results, the equation describing the fracture of adhesive joints as it was proposed by A. N. Gent and J. Schultz has to be extended. When that is done, it applies to viscoelastic adhesives, whether pressure sensitive or hot melts, and probably also to cross-linked adhesives. If G is the fracture energy of the joint, the equation G = G 0 + α K 2 ·va accounts for most experimental results and even for the fatigue of adhesive joints.

CLEAVAGE TOUGHNESS OF HETEROGENEOUS MATERIALS AND APPLICATION TO WELDED JOINTS

Abstract—Toughness is generally considered as a property of homogeneous materials. In this paper, the main interest is devoted to the cleavage toughness of multi‐materials. Weldments are a special case of these heterogeneous materials and are of great importance because of their wide applications. The case of a crack front intercepting more than one material is investigated experimentally and numerically. The agreement is generally very good. The special case of a brittle core zone located all along the crack‐tip is investigated only with numerical tools. However, a special feature arising from this study is that a critical HAZ size can be defined. Below this critical size, the failure probability should never exceed a selected value (e.g. 10%). This could be used as a design rule for multipass weldments.

最弱リンクモデルに基づく溶接部の局部劣化部じん性推定手法

Fracture toughness testing of heat-affected zone, especially grain coarsened zone, in welds is considerably difficult compared with weld metal and base metal, because the embrittlement of HAZ causes in the localized region. However, grain coarsened HAZZ is usually the most embrittled region in welds, it is often required to evaluate fracture toughness of its region itself.In the present paper, a probabilistic procedure for evaluating fracture toughness of the localized embrittlement region has been proposed newly, based on the weakest link model. By means of this procedure, distribution of cleavage toughness of localizedt embrittlement region, e.g. grain coarsened HAZ, is proved to be analyzed from test results on specimens of which notch is located in weld metal and base metal, respectively, and cross-bond-type notched specimens which have localized embrittlement region at notch front.Moreover, the sufficient number of cross-bond-type notched specimens which are necessary to evaluate fracture toughness of localized embrittlement region itself according to our present procedure has been investigated. By using 20 or more cross-bond-type notched specimens, cleavage toughness of the localized embrittlement region can be grasped.

The relationship between fracture toughness and Charpy impact transition temperatures in mild steel

A recently derived micromechanistically based expression is used to predict the cleavage fracture toughness of mild steel as a function of temperature for several different grain sizes. An upper bound to the cleavage-ductile transition temperature in toughness testing is estimated and a method for more accurate determination of the transition is outlined. The grain size giving the highest cleavage toughness is seen to vary with temperature in the range 4 – 15 μm. The Charpy impact test fracture appearance transition temperature (FATT) is also estimated for mild steel as a function of grain size. This is predicted to decrease with decreasing grain size down to a minimum at a grain size of 2 μm. Thus FATT and fracture toughness do not provide equivalent measures of a steel's resistance to cleavage fracture. The differences between these two fracture resistance parameters are believed to arise from two sources: the difference in strain rate and the different stress distributions at the starter defects. An empirical FATT-K IC correlation is used to predict the temperature dependence of the fracture toughness of mild steel for several grain sizes from the predicted FATT values. The toughness values so derived do not correspond directly to the micromechanistically based predictions.

Grain-size dependence of cleavage fracture toughness in mild steel

A MODEL has been proposed1 that relates the cleavage fracture toughness of a mild steel to its yield and fracture stresses through a microstructurally determined characteristic distance. This model quantitatively predicted the experimentally observed temperature dependence of the cleavage toughness in mild steels, and its applicability to low alloy steels has since been demonstrated2. In this study, an analytical crack tip stress distribution is combined with this model to provide an expression for the fracture toughness in terms of the microstructurally determined properties. Simply expressed grain size dependences of the yield and fracture stresses are used to predict the grain size dependence of the cleavage fracture toughness of mild steel—it is predicted that the toughness passes through a maximum at grain sizes in the region of 5 µm and that further grain refinement leads to reduced toughness.