Study of the relationship between fracture toughness (J IC) and bulge ductility

A theoretical model relating fracture toughness expressed as J _IC and bulge ductility {ie71-1} for a material exhibiting linear elastic behavior at low temperature and elastic-plastic behavior at higher temperatures is proposed. This model shows a variation of J _IC with {ie71-2} for linear elastic behavior and J _IC with {ie71-3} for elastic-plastic behavior. The model contains three constants to be determined experimentally for a given material, specimen geometry and testing conditions. A case study on 1045 steel in the temperature range ?60 to 25°C confirms the validity of the model. The experimental results help in determining the size of the fracture zone ahead of the crack as well as the mechanisms for crack blunting and crack growth.     

Effect of microstructure on the relationship between fracture toughness and ductility

The relationship between fracture toughness, expressed as J_IC, and ductility, given by measurements of the bulge ductility, was studied experimentally for two microstructures of 1045 steel. These microstructures consist of annealed pearlitic structure with hardness R_c = 15 and a tempered matensitic structure with R_c = 23. J_IC and bulge ductility measurements were performed in the temperature range of −100-25°C. The tensile properties at these temperatures were also obtained. The results show that the variation in flow stress with temperature is similar for both microstructures. However, the flow stress is higher, and the bulge ductility is lower, at a given temperature, for the martensitic structure. Also shifts in the transition temperature from linear elastic to elastic-plastic behavior are observed. Previously developed models by the authors describing the variation of J^IC with temperature and ductility are used to account for the behavior of the different microstructures examined.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the static fracture toughness of ductile structural steel

Fracture of ductile structural steels generally occurs after void initiation, void growth and void coalescence. In order for ductile fracture of structural steels to occur, energy must be spent to induce void initiation and void growth. Therefore, fracture toughness for ductile fracture should be contributed from void initiation and void growth. On the basis of this suggestion static fracture toughness (K_IC) of ductile structural steels is decomposed into two parts: void nucleation-induced fracture toughness (denoted as K_IC.n) and void growth-induced fracture toughness (K_IC.g). K_IC.n, defined as the stress intensity factor at which voids ahead of a crack begins to form, is calculated from crack tip strain distribution and void nucleation strain distribution. In contrast, K_IC.g is determined by the void growth from the beginning of void nucleation to void coalescence. Therefore, K_IC.g relates to the void sizes and void distribution. In this paper, the expression for K_IC.g is given from the void sizes directly from fracture surfaces. The relationship between K_IC.n, K_IC.g and K_IC is expressed in the form (K_IC)²=(K_IC.n)²+(K_IC.g)². The newly developed model was applied to the fracture toughness evaluation of three structural steels (SN490, X65 and SA440), and the theoretical calculation agrees with the experimental results.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

A model for the dynamic fracture toughness of ductile structural steel

We assume in this paper that the dynamic fracture toughness K_Id of ductile structural steels is dependent on void nucleation and void growth. The void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g were obtained by modifying the void nucleation-induced and void growth-induced static fracture toughness models, respectively, considering the effect of strain rate and local temperature. By the relationship between the void nucleation-induced dynamic fracture toughness K_Id·n and the void growth-induced dynamic fracture toughness K_Id·g((K_Id)²=(K_Id·n)²+(K_Id·g)²) dynamic fracture toughness K_Id could be quantitatively evaluated. With this model the dynamic fracture toughness of two structural steels (X65 and SA440) was assessed, and the causes for the differences between the static and dynamic fracture toughness were also discussed.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

The effect of annealing temperature on the fracture performance of isotactic polypropylene

The influence of annealing temperature on the fracture behaviour of a commercial extrusion-grade isotactic polypropylene was studied. Fracture mechanics analysis was carried out at room temperature and at a low crosshead speed underJ-controlled conditions. Parameters characterizing fracture initiation,J _IC, and crack propagation,T _M, were determined. Some thermal treatments induced “ductile instability” after a certain amount of crack extension while others strongly enhanced the fracture toughness parameters and promoted completely stable behaviour. Aiming to correlate mechanical properties with the supermolecular structure, the different morphologies induced by thermal treatments were studied by differential thermal analysis. In addition, a qualitative fracture surface analysis was carried out by SEM. Craze formation appeared to be the principal plastic deformation mechanism present. The degree of crystallinity and the degree of interconnection related to the thermal treatment the sample had undergone, are the main structural factors controlling fracture performance.     

Threshold toughness of polymers in the ductile to brittle transition region by different approaches

The fracture behavior of polymers in the ductile-to-brittle region is neither completely brittle nor entirely ductile. Besides, scatter in toughness results impairs the situation. Consequently, conventional methods based exclusively either on linear elastic fracture mechanics theory (LEFM) or on non-linear elastic fracture mechanics theory (NLEFM) are not suitable. It was demonstrated previously, that Weibull statistical method could be successfully used to determine the toughness threshold of polymers displaying ductile-to-brittle behavior. The present study compares the threshold toughness value determined by the statistical approach with other critical values calculated following other different suitable approaches: Low temperature plane strain fracture toughness, Plastic zone corrected fracture toughness, Stable and unstable propagation combined model, J extrapolated at zero stable propagation value, and Quasi J-R curve. The analysis was carried out on data points taken from fracture tests performed on polypropylene homopolymer, PPH, and on a blend of PPH and an elastomeric polyolefin, PPH/POes. The results of this analysis indicate that statistical, stable and unstable propagation combined model, and the J extrapolated at zero stable propagation value methods yield to very similar toughness threshold values being practically equivalent. In this case, threshold value was slightly smaller than the minimum J displayed by the experimental replicas, suggesting that it is an actual representative material toughness. Among these methodologies, the Statistical Method is applicable even if stable crack growth is difficult to determine. On the other hand, the methodologies based on LEFM tended to underestimate the fracture toughness, being very conservative while Quasi J-R curve method based on NLEFM overestimated the PPH/POes toughness value.     

Essential work of fracture compared to fracture mechanics—towards a thickness independent plane stress toughness

The essential work of fracture (EWF) and the J-integral methods were applied in a study of the effect of the thickness on the cracking resistance of thin plates. The paper discusses two themes: (1) the relationships between the two methods or concepts is elucidated, and (2) a new, thickness independent plane stress toughness parameter is proposed. For that purpose, cracked aluminium 6082O thin plates of 1-6 mm thickness were tested in tension until final separation. The EWF, w_e, and the J-integral at cracking initiation, J_i, increase identically with thickness except at larger thickness for which the increase of J_i levels off. J_i reaches a maximum for 5-6 mm thickness whereas w_e keeps increasing linearly with thickness. This difference is related to the more progressive development of the necking zone in front of the crack tip when thickness increases: at large thickness, cracking initiates well before the neck has developed to its stationary value during propagation. A linear regression on the fracture toughness/thickness curve allows partitioning the two contributions of the work of fracture: the plastic work per unit area for crack tip necking and a plane stress work per unit area for material separation. The pertinence of this new measure of the pure plane stress cracking resistance is critically discussed based on a micromechanical model for ductile fracture. The micromechanical void growth model incorporates void shape effects, which is essential in the low stress triaxiality regime.     

Anwendung des instrumentierten Kerbschlagbiegeversuchs zur Ermittlung von Referenztemperaturen nach dem Master‐Curve‐Konzept

Application of the Instrumented Impact Test for the Determination of Reference Temperatures Using the Master Curve Concept The instrumented impact test is suitable for the determination of fracture mechanical parameters. In this paper the determination of the dynamic fracture toughness values in the lower ductile‐to‐brittle transition region is presented. The fracture toughness is determined at the onset of cleavage fracture and evaluated by the Master Curve (MC) concept. The MC concept allows to quantify the variation of fracture toughness with the temperature within the lower ductile‐to‐brittle transition region. Limit curves of fracture toughness for defined failure probabilities and a reference temperature can be determined using this method. This paper presents the application of the master curve concept to the reference temperature determination through the thickness of reactor pressure vessel (RPV) steel plate. The reference temperatures determined dynamic fracture toughness values (T₀^dy) are compared with quasi‐static reference temperatures (T₀^st) and Charpy‐V transition temperatures (TT). T₀^dy, T₀^st and TT increase from the surface to the middle of the RPV steel plate. Compared with T₀^st, the T₀^dy values are higher approximately 70 to 90 K.     

Quantifying Tstress controlled constraint by the master curve transition temperature T0

Specimen size, crack depth and loading conditions may effect the materials fracture toughness. In order to safeguard against these geometry effects, fracture toughness testing standards prescribe the use of highly constrained deep cracked bend specimens having a sufficient size to guarantee conservative fracture toughness values. One of the more advanced testing standards, for brittle fracture, is the master curve standard ASTM E1921-97, which is based on technology developed at VTT Manufacturing Technology. When applied to a structure with low constraint geometry, the standard fracture toughness estimates may lead to strongly over-conservative estimate of structural performance. In some cases, this may lead to unnecessary repairs or even to an early “retirement” of the structure. In the case of brittle fracture, essentially three different methods to quantify constraint have been proposed, J small scale yielding correction, Q-parameter and the T_stress. Here, a relation between the T_stress and the master curve transition temperature T₀ is experimentally developed and verified. As a result, a new engineering tool to assess low constraint geometries with respect to brittle fracture has been obtained.     

Fracture toughness of grade D ship steel

Results from fracture mechanics tests on 15 mm thick grade D ship steel and weld are organised into a toughness distribution indexed to the Charpy 27 joule temperature, T_27J. The tests are carried out at 300 MPa√m/s to simulate the strain rate appropriate to a long (≈1 m) through thickness crack in the deck of a ship under storm conditions. Most of the data are in the brittle to ductile transition region and end in cleavage fracture. A best fit to the data is found using the exponential curve fit (ECF) method. Lack of censoring of invalid results means that the trend line is not a true ‘plane strain’ fit. It is argued that inclusion of ‘plane stress’ data makes the resultant toughness distribution more relevant to ship fracture predictions. Equations are presented which allow the toughness to be plotted at any chosen probability level as a function of temperature relative to T_27J. A safe lower bound to the data is given by the 0.1% probability trend assuming that T_27J for grade D plate and weld is no higher than −20 °C. The data are also used to propose that it is impossible to generate an elastic ductile tearing instability in ship steel with Charpy upper shelf values of 100 J or more.     

The use of master curve method for statistical re-evaluation of surveillance test data for WWER-1000 reactor pressure vessels

The surveillance fracture toughness test data for WWER-1000 reactor pressure vessel materials from Ukrainian nuclear power plants were re-evaluated using the Master curve methodology. It has been shown that experimental temperature dependence of fracture toughness parameters and a scatter of K_Jc values are in a good agreement with a Master curve shape and 5 and 95% tolerance bounds for materials in unirradiated condition and after neutron irradiation up to fluence 41. 2·10²² n/m² (E > 0.5 MeV). For the Khmelnitsky nuclear power plant unit 1 reactor pressure vessel an analysis has shown that normative approach PNAé G-7-002-86 underestimates essentially the measured fracture toughness of unirradiated weld metal. The reference temperature T₀ calculated according to the Master curve method was compared with a critical brittleness temperature T_K0 for reactor pressure vessel materials in unirradiated condition. It has been found that temperature T₀ is much lower than T_K0 . Furthermore a difference between T₀ and T_K0 values varies essentially from one material to another. A correlation between temperatures T_{28 J} defined from Charpy energy curve and T₀ values calculated from precracked Charpy specimens test was obtained. The analysis has shown that the results based on precracked Charpy specimens can provide nonconservative assessment of fracture toughness for WWER-1000 reactor pressure vessel materials.     

Influence of specimen size and microstructure on the fracture toughness of a martensitic stainless steel

The fracture toughness of alloy HT-9,² a martensitic stainless steel under consideration for fast reactor and fusion reactor applications, was determined from circular compact tension specimens using the multi-specimen R-curve method. Specimens with thicknesses of 11.94, 7.62 and 2.54mm and widths of 23.88 and 11.94 mm were tested to investigate the effects of specimen size on fracture toughness. The test results obtained from all specimens are in good agreement and thickness requirements for a valid J_1c test are satisfied. The experiment indicates that small specimens of HT-9 may be used for post-irradiation fracture toughness testing.Fractographic examination of the fracture surfaces reveals that fracture in HT-9 is significantly influenced by delta ferrite stringers present in the material. The fracture surface examination and crack opening displacement measurements for specimens tested at various temperatures are consistent with the temperature dependence of the J_1c results.     

Fracture toughness and thermal shock of tool and turbine ceramics

The behaviour of some commercial tool carbides and turbine ceramics has been investigated in regard to resistance to crack initiation, crack propagation and retained strength after thermal shock. New data are provided, particularly measurements of the fracture toughness of these materials at actual operating temperatures (up to 1200° C). Many of the materials did not follow the generally accepted Hasselman theory for thermal shock in ceramics, and instead of showing a discontinuity in retained strength at some critical quenching temperature difference, their residual strengths fell gradually at temperatures lower than their supposed critical quenching temperature. This behaviour is explicable when high temperature toughnesses, strengths and moduli are used in the damage resistance parameter (ER/gs _f ² ). It seems that materials not following the Hasselman model suffer cumulative damage with increasing number of shocks. Sub-critical crack growth occurs even if (K _IC/gs _f)² values are constant, and such damage, which reduces the room temperature retained strength, is enhanced by (K _IC/gs _f)² decreasing at temperatures below ΔT _c. In contrast, materials obeying Hasselman's model appear to have a constant (K _IC/gs _f)² below ΔT_c and for some temperature range above. Only then are “one-shock“ characterizations of materials possible, otherwise, the retained strength depends upon the number of prior shocks. Experiments are also reported which describe the effects of rate of testing on the unshocked and shocked mechanical properties of ceramics. Oxidation is shown to influence the results in a manner not obvious from single shock tests.     

Experimental correlation between ductility and J-integral in the transition region of 1045 steel

A study of the variation of fracture toughness j_IC and ductility, measured under both tensile loading and biaxial plane strain (bulge) loading, of AISI 1045 steel in the annealed condition, in the transition temperature range of ?60 to 25°C was carried out. This temperature range delineates the changes in behavior from linear elastic to elastic-plastic behavior for this steel. It was found that the variation of j_ic with temperature shows a transition at about ?20°C while the bulge ductility only has a marked transition below ?40°C. These trends are explained in terms of the effect of material properties, namely the flow stress, on crack blunting, while the bulge ductility is correlated with the total strain to cause significant crack growth to take place. In the elastic-plastic region, a linear relationship between j_IC and bulge ductility was found to occur.     

Use of COD in KIC determination

It has been theoretically postulated that the crack opening displacement (COD) technique is applicable in characterising fracture of material in the generally yielded as well as linear elastic regimes. Hence, it is possible to determine the plane strain fracture toughness, K_IC, of a material using the COD method if the onset of crack propagation and the location of the centre of rotation can be evaluated. In the present investigation, COD values at crack initiation, δ_i, for Rochling Moulrex A steel were obtained with 3-point bend specimens at six different tempering temperatures using the multiple specimens load-unload extrapolation technique. It is found that by using the BS 5762:1979 analysis, K_IC values were grossly over-estimated. The use of a constant rotational factor is observed to be inadequate. Under small scale yielding conditions, the centre of rotation is postulated from the present results to be located at approximately the end of the stretched zone. This supposition was applied to estimate the K_IC values of standard compact tension specimens made from Rochling Moulrex A, Assab 25X and Comsteel En25 steels. Where the material was linear elastic, the estimation was good with discrepancy of less than 7%. Overestimation was seen at high tempering temperatures due to the increasing amount of plasticity in the material that shifted the location of the centre of rotation from the end of the stretched zone to a position closer to that suggested in the British Standard.     

Viscoelasticity of ceramics at high temperatures

The dependence of the fracture toughness, K _IC, on the loading rate has been calculated. On the basis of linear elastic fracture mechanics (LEFM) a strong dependence of the fracture toughness on the loading rate is obtained if subcritical crack growth is taken into account. If the subcritical crack growth parameters n and B are sufficiently small, which correspond to a high velocity of crack extension, the fracture toughness should decrease at lower loading rates. This behaviour is similar to the well-known decrease of bending strength. The experimental results for alumina containing glassy phase as a model material, however, show a maximum in a certain regime of loading rates. A model is established, which combines LEFM and the viscoelasticity, and leads to a maximum of K _IC at a certain loading rate dependent on the viscosity of the glassy phase.