Effects of microstructure, specimen and loading geometries on KIC of brittle honeycombs

Fracture toughness of brittle honeycombs depends on cell microstructure, specimen and geometries. A microstructure coefficient in the K_IC expression of brittle honeycombs can not be found analytically. In this paper, a finite element program is utilized to numerically determine the coefficient. In practice, fracture toughness can be measured from conducting a three-point bend or uniaxial tension test. Specimen geometry restrictions of three-point bend test for honeycombs are examined and proposed here. Meanwhile, fracture toughness of honeycombs under the two loading geometries is compared; results show that K_IC measured from uniaxial tension test is smaller than that from three-point bend test if the K_IC formulations for solid materials are employed. As a result of that, the K_IC formulation of three-point bend test is modified for honeycomb-like materials.     

The mixed mode I/II fracture behaviour of lightly tempered HY130 steel at room temperature

The mixed mode I/II fracture behaviour at room temperature of HY130 steel tempered at 350°C has been investigated using edge-cracked bend bar specimens loaded in anti-symmetric and symmetric four point bend configurations. In all cases fracture occurred by a localized shear decohesion mechanism that could not be characterized by the stress intensity factors, K_I and K_II, but for which the crack tip displacements, δ_I, and δ_II, appear to provide a first level of characterization. The results suggest that fracture is described by a maximum shear criterion, and this is consistent with the present understanding of fibrous fracture micro-mechanisms in the material.     

Comparison of fracture toughness test procedures for aluminum alloys

The Dynamic Tear (DT) test permits the measurement of fracture propagation energy across the toughness spectrum for metals which are definable by linear elastic analyses to those requiring gross plastic strains for fracture. The linear elastic fracture mechanics parameter K_ic provides a relationship between critical flaw size and stress level at which crack instability will occur. Unlike the DT test, the K_ic toughness test cannot be utilized for fracture under conditions of elastic-plastic or gross plastic strain.

A correlation has been developed between the DT test and the K_IC parameter for ahuminum alloys. The relationship may also be expressed in terms of β_ic-DT and _ic-DT. The K_ic values were determined with several specimen types and a comparison of the values for different specimens is provided.

The correspondence between K_ic and DT serves several purposes. It provides a frame of reference for DT values obtained from frangible metals that fracture under linear elastic conditions. Accordingly, it permits utilization of the inexpensive DT test to approximate the flaw size-stress instability conditions which otherwise must be determined by the more expensive K_ic test. Furthermore, through extrapolation, it is possible to utilize the DT test to estimate the critical flaw size under an elastic-plastic strain field.     

Determining KI of a V-notch from the existing results of a linear crack

Based on theoretical analysis and a hypothesis, a new method is given for determining K_I of a V-notched plate under various boundary conditions. By means of this method, the stress intensity factor of a V-notch can be easily obtained from the existing results of a linear crack. Examples show this method is both reasonable and reliable.     

Kic Transition-temperature behavior of A517-F Steel

Linear-elastic fracture mechanics has been widely used to obtain K_ic values on very-high-strength steels (yield strengths > 200 ksi) that generally do not exhibit a ductue-to-brittie transition in failure mode as a function of temperature. However, as the use of the K_ic test approach is extended to those steels that do exhibit a ductile-to-brittle transition, information on the K_ic transition-temperature behavior of steels is required. Therefore, to establish general relations between K_ic and Charpy test results, slow-bend K_ic fracture tests and various Charpy tests were conducted on A517-F steel at temperatures between −320 and +80°F.

The results indicated that a plane-strain K_ic température transition does exist for A517-F steel. Furthermore, this transition occurred in the same temperature range (−150 to −50°F) as the transition denned by slow-bend Charpy test results for fatigue-cracked specimens. In both the K_ic tests and the Charpy tests, the transition-temperature behavior appeared to be related to a gradual change in the microscopic fracture mechanism. The upper shelf, as denned by slow-bend Charpy tests, appeared to be a region in which K_ic values cannot be obtained, regardless of specimen geometry, because of general yielding and crack blunting.

A procedure is proposed in which the dynamic K_ic behavior of a material can be predicted from static K_ic test data by shifting the static K_ic values along the temperature axis by the same amount as the static Charpy energy values are shifted by impact testing.

In general, the results of this investigation have demonstrated that a transition in K_ic behavior of A517-F steel does exist as a fution of temperature and that that transition is independent of the K_ic to K_c stress-state transition.     

Exploring the fracture toughness KIE and KIC of a medium-Strength steel plate using the surface-flaw test

The fracture toughness of a 30 CrMnSiA steel plate of three thicknesses (10,8 and 5 mm) and three widths (110,80 and 56 mm) has been investigated by using surface-flaw method under room temperature. It is not easy to compute the value of K_IE by the maximum applied load. But the values of K_IE and K_IC could be obtained easily, if the computation of the conditional applied load P₁₀ and P₅ based on the relative effective extension Δa/a₀ = 10% and 5% were adopted, together with the conditions of P_max/P₁₀ 1.2 and P_max/P₅ 1.3. The K_R — Δ_a curve, i.e. the resistance-curve described by the parameter K, has been plotted. The values of K_IC and K_IE are then the resistances corresponding to the real extensions of flaws of Δ/a₀ = 2 and 7%, respectively. These values so obtained are in good agreement with the computed values of K_IC and K_IE by using the conditional applied loads. The values of K_IC and K_IE so obtained are also in agreement with the value of K_IC converted from the J-integral and the effective value of K_IE computed by the maximum applied load, respectively.

An approximate relation between K_IC and K_IE has been found to be: K_IC = (0.85˜0.95)K_IE.

The requirements for the dimensions of specimens are: Thickness of plate: B 1.0(K_IC/σ_0.2)² or 1.25(K_ICσ_0.2)²]; Width of plate: 8 W/B 10, 4 W/2c 5; Effective length: l 2W.     

Fracture toughness of turbine-generator rotor forgings

A comprehensive program is being conducted relative to applying fracture mechanics technology to large turbine-generator rotors. One facet of this program involves the determination of plane-strain fracture toughness (K_Ic) over a range of temperatures for various types of rotor steels. Data have been obtained for ten large production forgings, representing three alloys, using various types of compact K_IC and spin burst test specimens. These results demonstrate that valid K_IC data can be obtained in these types of intermediate-strength, high-toughness steels in the temperature range of practical interest. Data indicate that the plane-strain fracture toughness of these steels increases rapidly with increasing temperature and is rather high (K_tc/σ_YS > 1 in^1/2), in the application range. As a result, the critical defect sizes for catastrophic failure upon a single cycle of loading are relatively large. The plane-strain fracture toughness measurements, as well as the application of these data, are presented and discussed.     

Theoretical and experimental study of superimposed fracture modes I, II and III

The authors wish to present an all-fracture mode specimen with which it is possible to conduct fracture mechanics tests for pure mode I, pure mode II, pure mode III, as well as for all possible combinations of the above-mentioned. By means of a finite element analysis of this specimen, the stress intensity factors K_I, K_II, and K_III were computed. It was discovered that K_II and K_III are coupled for in-plane shear and anti-plane shear loading, i.e. a mixed state occurs locally. The integral mean along the crack front yields however only to a K_II factor for in-plane shear and to a K_III factor for anti-plane shear loading. Fracture experiments under mixed-mode loading, using this new specimen, demonstrate the influence of the loading type on the orientation and on the structure of the fracture surface.     

Hardness, internal stress and fracture toughness of epitaxial AlxGa1−xAs films

Vickers microhardness indentations of 10 μm (001) oriented epilayers of Al_xGa_1−xAs on GaAs substrates have been utilized to evaluate the hardness H_v, the internal stress, and the fracture toughness K_Ic of the layers as a function of their composition parameter x. The hardness H_v varies linearly according to: (6.9-2.2x) GPa and K_Ic increases linearly with x according to: K_1c = (0.44+1.30x) MPa m^1/2. The influence of the substrate on these measurements was found to be negligible for the layer thickness (10 μm) and the indentation load (0.25 N) used, disregarding internal stresses.

Internal film stresses were evaluated by the bimorph buckling method, and were found to depend on the composition parameter according to σ = 0.13x GPa. These stresses did not notably affect the H_v measurements, but for K_Ic corrections as large as 25% had to be made.

The radial cracks observed were of the shallow Palmqvist type. In contradiction to previous reports on this type of cracking, it was found to initiate during unloading, not during loading, and a physical explanation for this deviation is given. No deep radial/median cracks were observed. It was found important to use expressions based on the correct crack geometry in the K_Ic evaluation. Also, a simple theory for the influence of internal stresses on the K_Ic results has been developed.     

Studies on fracture toughness and fractographic features in Fe---Mn base alloys

Fractographic examinations of fracture surfaces of single edge crack plate tension fracture toughness test specimens of some new Fe---Mn base maraging alloys have been conducted. The interrelations between the fractographic features, fracture toughness and other mechanical properties of these alloys have been studied. It is observed that the width of the stretched zone between fatigue and rapid fracture is related to K/σ_ys of the material where K is either K_IC, K_Q or the stress intensity for onset of microscopic slow crack growth. The stretched zone width is approximately equal to the average dimple size. Also it is of the order of the process zone size (calculated by modified Krafft's model) and the critical crack opening displacement in plane strain condition. Hahn and Rosenfield's model to estimate K_Ic was found to show much higher values in those cases where the fracture mode was predominantly cleavage, quasicleavage or intergranular.     

Fracture behavior of cross-ply graphite/ epoxy laminates

Fracture behavior of cross-ply (0/90)_4s, (0/90)_10s, (0₂/90₂)_2s and (0₄/90₈/0₄)_T laminates of T300/934 graphite/epoxy material was studied using compact tension specimens of several widths and thicknesses, center notched tension and three point bend specimens. The process of damage initiation and propagation was studied and is discussed in detail. The critical stress intensity factor was evaluated and its variation with specimen size and type is shown. On the basis of these investigations, a suitable specimen for the evaluation of meaningful fracture toughness is suggested.     

Effects of crack growth on the load-displacement characteristics of precracked specimens under bending

A critical evaluation of the feasibility of obtaining crack growth parameters from quasi-static bend tests is presented. First derived are the governing differential equations which characterize the time-history of bend test parameters for a given elastic material exhibiting power law crack growth behavior v = v_max(K_I/K_IC)^N. A numerical solution scheme is then developed which is capable of solving the initial value problem, thus quantitatively assessing the influence of crack growth on the load-displacement output. The results of this analysis indicate that in order to calculateK_IC accurately based on the peak load data, the loading rate has to be set sufficiently fast compared to v_max (but below dynamic rates), otherwise, it will generally overestimate its true value whenever slow crack growth occurs during the test; and that for high N materials the flexural test method gives a broad error band inN prediction and hence is not a reliable technique. However, it can be used by a designer to quickly screen the new materials with high Nvalues which are potential candidates for structural application.     

A comparison on the effect of the ratio a/w on the fracture behaviour between ductile and brittle materials

The effect of the ratio a/W on the fracture behaviour of ductile and brittle materials has been studied by measuring the crack-opening displacement and J-integral for ductile material and the stress intensity factor for brittle material in three-point bend specimens with shallow and deep notches. It is shown that, for ductile material, the values of δ_i and J_i, for specimens with shallow notches are larger than those of deep notches. On the contrary, for brittle material, the values of K_IC for specimens with shallow notches are smaller than those of deep notches. The reason for this is explained.     

Influence of specimen size and configuration on the plastic zone size, toughness and crack growth

The main purpose of this investigation is to evaluate the effect of the thickness, width, aspect ratio and geometry of the fracture toughness specimen on the resultant displacement due to growth of plastic zone and crack.

The analytical part evaluates the effect of the width, aspect ratio, geometry and flow properties on the displacement due to the growth of plastic zone as well as the crack. The experimental part evaluates the effect of thickness and width of a compact tension specimen on the displacement and on the thickness direction contraction due to the growth of the plastic zone.

The main result of the investigation is that the plastic zone size decreases and the constraint to yielding increases as the width of a CT specimen increases. Based on this and other analytical and experimental result, a new procedure for the determination of K_IC has been proposed. The procedure is verified by experimental data obtained by other workers. The procedure overcomes the limitation of ASTM E399 for the determination of K_IC.     

Estimation of fracture toughness of steel using chevron notched round bar specimens

A generalized methodology has been outlined in this paper for estimating the minimum normalized stress intensity factor (Y*_min) of chevron notched round bar specimens, subjected to three‐point bend loading. Using such specimens, a series of fracture toughness tests have been carried out for the first time on two steels. The major inferences drawn from this investigation are: (i) reproducible fracture toughness values can be achieved using chevron notched rod specimens of identical configuration and (ii) the estimated magnitudes of fracture toughness obtained by using chevron notched rod specimens are in good agreement with those achieved by using chevron notched rectangular bar specimens of the same material.     

Evaluation and analysis of interlaminar fracture toughness of bead filled matrix hybrid composite materials using orthotropic fracture mechanics

Evaluation of Mode I interlaminar fracture toughness for unidirectional hybrid composites fabricated with a bead filled epoxies was carried out. The two important fracture toughness parameters, G_IC and K_IC values of hybrid composites, were reviewed in accordance with the orthotropic fracture model. The deviation of measured G_IC and K_IC values from predicted values were explained based on the critical review of the basic assumption of orthotropic fracture model and characteristic material properties of hybrid composites. It can be said that, basically, the orthotropic fracture model can be used for evaluation of hybrid composite materials. However, careful analysis for G_IC and K_IC values which were derived from different source and some correction factor for K_IC values are necessary.     

A more exact determination of the JIc-integral fracture toughness values obtained by compact tests

Fracture toughness K_JIc values, determined on standard compact specimens by the use of modified equations of Rice, Paris and Merkle, and Merkle and Corten, are presented. The equations permit elimination of errors caused by inaccuracies in the loadline displacement measurements, and they can be applied not only for deeply cracked specimens but also for a wider range of ratios a/W. Experimental results, obtained on two low strength steels using 75 and 40mm thick specimens, showed a very good agreement between the K_JIc values calculated by both equations. These values do not differ by more than 2%.     

Dynamic fracture toughness parameters for HY-80 and HY-130 steels and their weldments

Lower bound dynamic fracture toughness parameters for HY-80 and HY-130 steel and their weld metals are identified. Specific values of the parameters K_Id and K_Im obtained from direct measurements are reported together with estimates inferred from the large body of Charpy energy, nil ductility transition temperature and dynamic tear energy measurements. The emphasis is on reasonable lower bound values at 30°F, the lowest anticipated service temperature, for use in elastodynamic analyses of crack growth initiation, propagation, and arrest in ship structures. For these conditions, it has been found that the ratio K_Id/ σ_Y is approximately equal to 2 in^1/2 for HY-80 steel. For HY-130 steel and the HY-80 and HY-130 weld metals under these same conditions, K_Id/ σ_Y is approximately 1 in^1/2. Consequently, HY-80 plate appears to be substantially more resistant to fracture under dynamic loading than are the other three grades examined.     

Dynamic fracture toughness of X70 pipeline steel and its relationship with arrest toughness and CVN

The dynamic fracture toughness K_1d and J_1d, arrest toughness K_1a and Charpy V-notched impact toughness (CVN) of a pipeline steel, X70, were studied at different temperatures. It was found that fracture toughness was strongly affected by temperature and loading rate. The fracture toughness decreases with decreasing temperature from 213 to193 K and increasing loading rate from to . At constant temperatures, only increasing loading rate can induce the transition from ductile to brittle. There exists a fracture transition caused by loading rate. Through thermal activation analysis, a quantitative relationship has been derived:

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. It can describe the fracture process at different temperatures and loading rates. At a loading rate of , the relationship can predict arrest toughness well. It provides the possibility of measuring arrest toughness with small size specimen. An empirical equation has been derived: CVN=4.84×10⁶T^−2.8K_1d(K_1a), which correlates K_1d and K_1a with CVN in one equation. This means that we can calculate K_1d and K_1a when we get CVN.