Unloading Elastic Compliance Method Research Articles

A study of automatic measurement method of RPG (Re-tensile Plastic zone’s Generated) Load

ABSTRACT Identification of the relationship between fatigue crack propagation rate (da/dN) and stress intensity factor range (∆K) is inevitable to apply the fracture mechanics approach to assess the growth of fatigue crack growth. The relationship between da/dN and ∆K is widely applied to evaluate fatigue crack propagation behaviour. To evaluate the fatigue crack growth history under variable loading history, it is necessary to replace ∆K to the effective stress intensity factor range, which can quantitatively consider fatigue crack opening and closing behaviour. ∆K eff proposed by Elber is well known as the effective stress intensity factor range, but even if ∆K eff is applied to evaluate the fatigue crack propagation behaviour, a threshold value ((∆K eff)th) was occurred. On the other hand, it is known that fatigue cracks propagate even at ∆K eff below (∆K eff)th under variable loading history. This implies that ∆K eff is an insufficient parameter to describe fatigue crack propagation behaviour. ∆K RPG, which has a close relationship with the cyclic plastic behaviour in the vicinity of the crack tip proposed by Toyosada and Niwa, can overcome the shortcomings of ∆K eff even under complicated variable loading history including multiple frequency components. To apply the fatigue crack propagation law with ∆K RPG as a parameter, it is necessary to experimentally measure the RPG load and identify the propagation law constants (∆K RPG = C(∆K RPG) m ) C and m. A conventional method for identifying RPG loads requires the superposition of the hysteresis loop near the crack tip and its reversal loop as measured by the unloading elastic compliance method. However, advanced skills in this method, such as understanding the characteristics of measurement errors associated with loops, is required. In this study, we have proposed an automatic method for measuring the RPG load that is equivalent to manual measurement results by an expert and we have validated the automatic measurement method by comparing the results of automatic measurement using our proposed method with the past conventional measurement results for several materials and loading conditions.

Numerical simulation of fatigue crack propagation: A case study of defected steam pipeline

In order to prevent the premature failure of steam pipeline produced of molybdenum-vanadium steel, the experimental tests were performed to measure fracture toughness and to determine the mechanical behaviour of cracked pipes. A finite element method was used to calculate the fracture behaviour of the pressurized pipeline made of 14MoV6-3 steel based on the J-integral computation. The J-R curves were experimentally obtained by the elastic unloading compliance method for the single edge notched bend specimens and compared with those obtained using finite element method.A two dimensional finite element analysis was performed in Ansys Workbench software to determine the stress distribution and calculate J-integral values for the selected specimen geometry. Special attention was paid to the influence of applied boundary conditions on the accuracy of J-integral values, as well as to the influence of mesh density. It is shown that numerically obtained J-values significantly depend on the number of nodes used to apply displacements. However, if recommendations proposed in this paper are implemented, the accuracy of calculated values is satisfactory and successful failure analysis can be carried out. This approach can be useful in engineering applications where time saving and costs reducing are required.

Evaluation of fracture toughness in different regions of weld joints using unloading compliance and normalization method

Both unloading compliance method and normalization method specified in ASTM E1820-16 were conducted on the API 5L X70 and X80 pipeline steels. Extensive experimental measures of fracture toughness for different regions of weld joints were carried out. For comparison, the J–R curves and initiation fracture toughness determined using the normalization method are compared with those obtained by the elastic unloading compliance method for two different weld joints. The results show that good agreements exist between the two methods, and an average difference less than 10% is detected. Moreover, the comparison indicates that the J–R curves from the unloading compliance method are lower at the initial stage of crack extension, and as the crack grows, the J–R curves are higher compared with those of the normalization method. For different regions in weld joints, there is clear distinction of differences between the corresponding results from above two methods. A ductile brittle mixed fracture mechanism is found in weld metal and coarse grained heat affected zone, and a corresponding higher deviation is detected.

ボロン添加ステンレス鋼の破壊じん性に及ぼすひずみ速度の影響

Fracture toughness tests were performed for borated stainless steel in the present study. Fracture resistance curves were determined by the unloading elastic compliance method based on the ASTME1820 as well as an image processing technique. The latter was applied to investigate the effect of strain rate on the fracture toughness using split Hopkinson bar method.

Fatigue Crack Growth Behavior of FSWed Joint Joined with a Bobbin Type Tool in Different Aluminum Alloys

Fatigue crack growth (FCG) behavior at weld nugget zone (WNZ) and heat affected zone (HAZ) in friction stir welded (FSWed) joints joined by using a bobbin type tool in 5052, 6N01 and 7N01 aluminum alloys were investigated comparing to the base materials (BM). Constant stress amplitude fatigue crack growth tests were conducted with stress ratio of 0.1. Crack closure behavior was investigated simultaneously during fatigue test with unloading elastic compliance method. The results in this study showed that in near threshold region, FCG resistance in WNZ of FSWed 5052 and 6N01 joints was lower than that in the BM and the HAZ. In contrast, FCG resistance in WNZ of FSWed 7N01 joint was higher than that in the BM and the HAZ. At high ΔK region, WNZ of FSWed 5052 joint had the similar FCG resistance with the BM and the HAZ. However, WNZ of FSWed 6N01 joint showed lower FCG resistance compared to the BM and the HAZ. FCG resistance in WNZ of FSWed 7N01 joint was the similar with that in the HAZ but was lower than that in the BM. Crack closure behavior was observed in BM and HAZ for all materials tested. In WNZ, crack closure was found in FSWed 7N01 joint but was not found in FSWed 5052 and 6N01 joints. Difference in FCG behavior at different weld region was mainly due to difference in crack closure behavior in FSWed 5052 and 6N01 joints. However, in case of FSWed 7N01 joint, it is considered that effect of microstructure was significant on FCG behavior even at high ΔK region.

Improved Incremental J-Integral Equations for Determining Crack Growth Resistance Curves

The J-integral resistance curve is the most important material properties in fracture mechanics that is often used for structural integrity assessment. ASTM E1820 is a commonly accepted fracture toughness test standard for measuring the critical value of J-integral at the onset of ductile fracture and J-R curve during ductile crack tearing. The recommended test procedure is the elastic unloading compliance method. For a stationary crack, the J-integral is simply calculated from the area under the load-displacement record using the η-factor equation. For a growing crack, the J-integral is calculated using the incremental equation proposed by Ernst et al. (1981, “Estimations on J-integral and Tearing Modulus T From a Single Specimen Test Record,” Fracture Mechanics: Thirteenth Conference, ASTM STP 743, pp. 476–502) to consider the crack growth correction. For the purpose of obtaining accurate J-integral values, ASTM E1820 requires small and uniform crack growth increments in a J-R curve test. In order to allow larger crack growth increments in an unloading compliance test, an improved J-integral estimation is needed. Based on the numerical integration techniques of forward rectangular, backward rectangular, and trapezoidal rules, three incremental J-integral equations are developed. It demonstrates that the current ASTM E1820 procedure is similar to the forward rectangular result, and the existing Garwood equation is similar to the backward rectangular result. The trapezoidal result has a higher accuracy than the other two, and thus it is proposed as a new formula to increase the accuracy of a J-R curve when a larger crack growth increment is used in testing. An analytic approach is then developed and used to evaluate the accuracy of the proposed incremental equations using single-edge bending and compact tension specimens for different hardening materials. It is followed by an experimental evaluation using actual fracture test data for HY80 steel. The results show that the proposed incremental J-integral equations can obtain much improved results of J-R curves for larger crack growth increments and are more accurate than the present ASTM E1820 equation.

Fatigue Crack Growth and Closure of Stainless Casting SCS6 and Carbon Steel Casting SC49 for Hydraulic Turbine Runner

In hydraulic turbine runner, unexpected accidents due to fatigue often occur. In this study, in order to clarify fatigue crack growth and closure properties on SCS6 and SC49 used as hydraulic turbine runner over 27 years, fatigue crack growth test under the stress ratio R-constant were carried out using compact tension specimens of both materials. Fatigue crack growth rate and crack closure were measured by means of an unloading elastic compliance method. The results are summarized as follows:(1) Although the stress ratio dependency on the fatigue crack growth rate is found in both materials, the influence is recognized remarkably in SCS6 except for threshold value. (2) Although the threshold stress intensity factor ΔKth of SCS6 is almost same as that of SC49 when R<0.5, the value of stress ratio of SCS6, when the R-dependency of growth rate disappears, was found to be higher than that of SC49. (3) Fatigue crack growth rates of SCS6 and SC49 could be correlated with the effective stress intensity factor range ΔKeff, and da/dN-ΔKeff relationships of both materials agree well in the low and mid growth rate region except for threshold value. In high ΔKeff, however, the rapid acceleration of crack growth rate due to the change of growth mechanism to cleavage fracture was found only in SC49.

Fatigue properties and crack propagation behavior of stainless cast steel for turbine runner of hydraulic power generation

In order to clarify the fatigue properties of stainless cast steel JIS SCS6 used as the turbine runner of hydraulic power generation for about 27 years, fatigue tests were carried out by using tension-compression specimens, plane bending specimen and CT specimens. The results are summarized as follows: The fatigue strength of tension-compression was lower than that of plane bending. In order to examine the reason for that, fracture surfaces were observed by SEM. It is because that in the case of tension-compression fatigue tests, the increase of volume of dangerous layer which was applied high stress led the increase of the size of the casting defect included there for the loading mode and the shape of specimens. It suggests that casting defects strongly affect the fatigue properties of aging stainless cast steel. Furthermore, according to the estimation of fatigue life, it is clear that fatigue life of aged stainless cast steel can evaluate by using the casting defect size at crack initiation site and the stress intensity factor calculated by defect size. In addition, to clear the fatigue crack propagation behavior, the relationship between the fatigue crack growth rate and effective stress intensity range was examined by using the unloading elastic compliance method which can observe the detailed fatigue crack closure behavior.

Experimental Estimation of J-R Curves from Load-CMOD Record for SE(B) Specimens

Abstract Fracture resistance of ductile materials is often characterized by a J-R curve, and measured using the fracture toughness testing standard ASTM E1820 (Standard Test Method for Measurement of Fracture Toughness). The recommended elastic unloading compliance method or resistance curve test method requires simultaneous measurements of applied load (P), load-line displacement (LLD), and crack-mouth opening displacement (CMOD) from a single test for the single-edge notched bend [SE(B)] specimen. The P-CMOD record is used to determine crack extension, and the P-LLD record in conjunction with the crack extension is used to calculate the J-integral. However, it is well known that while highly accurate CMOD measurements can be made, the measurement of LLD is less accurate and more difficult because of transducer mounting difficulties, specimen load point indentions and load train deflections, or a combination thereof. Extensive finite element analyses showed that the LLD-based J equation may give inaccurate results for a shallow-cracked SE(B) specimen because its geometry factor η may depend on the strain hardening exponent. In contrast for the same geometry, the CMOD-based η factor is insensitive to the hardening exponent, and thus a CMOD-based J equation could be more accurate to be used in the determination of J-R curves. Based on the energy principle, this paper proposes a CMOD-based J equation for a growing crack using an incremental function similar to the present ASTM E1820-06 formulation that is applicable to the J calculations for a J-R curve testing. The proposed CMOD-based J formulation contains two geometry factors, i.e., CMOD-based η and γ, and can consider the crack growth correction. The solutions of four geometry factors are presented for the SE(B) specimens with a wide range of crack length. The proposed formulation is then applied to determine J-R curves for HY80 steel using the load-CMOD record for SE(B) specimens, and the results are compared with those using the traditional LLD-based formulation. The comparison shows close agreement between these two formulations. It is recommended that the proposed formulation be used in ASTM E1820 to determine more accurate J-R curves and reduce test costs as well.

J–Resistance curve testing of HY80 steel using SE(B) specimens and normalization method

The normalization method is adopted for standard and nonstandard specimens in this paper to develop J– R curves for HY80 steel directly from load versus load-line displacement records without use of automatic crack length measurement. The standard specimens usually contain high crack-tip constraints, while the nonstandard specimens involve low crack-tip constraints. To obtain J– R curves with different constraints, a series of single edge notched bend (SE(B)) specimens with different crack lengths for an HY80 steel are tested in accordance with ASTM standard E1820. The normalization method is then used for determining crack extension and J– R curves for these SE(B) specimens. To validate the normalization method, the J– R curves determined using the normalization method are compared with those obtained by the elastic unloading compliance method for the SE(B) specimens. The comparison shows that good agreements exist between the two methods, and the normalization method is a viable tool to be used to determine J– R curves of the HY80 steel for the standard as well as nonstandard SE(B) specimens. In the J-integral calculations, the resistance curve test method, the basic test method and the modified basic test method specified in ASTM E1820 are evaluated. The results indicate that the modified basic method can be equivalent to the resistance curve method.

Fatigue Crack Growth Behavior of Ti-6Al-4V Alloy with Bimodal Microstructure under Repeated Two-step Load Sequences

The effect of microstructure on fatigue crack growth behavior under repeated two-step load sequences was investigated using compact tension specimens of Ti-6A1-4V alloy with bimodal microstructure. Fatigue crack growth rate and macroscopic crack closure were measured by means of an unloading elastic compliance method. The da/dn-ΔKeff relationship exhibited a trilinear form in so-called Paris region corresponding to the change of growth mechanism from the intergranular fracture in the low ΔKeff region to the transgranular one in the high ΔKeff region. The crack opening point, Kop, was constant during one block of varying loading in the case that the crack extension during one block loading was relatively short. On the other hand, in the case that the crack grew beyond the cyclic plastic zone introduced by ΔKH, Kop under low level loading decreased from the initial high value to the stationary low one as the crack grew. Depending on the test conditions, the fatigue crack growth rate under varying loading was found to be higher or lower than that estimated by da/dn-ΔKeff relation under constant amplitude loading, which indicates that the load variation resulted in both crack grown acceleration and deceleration in terms of ΔKeff. The crack growth acceleration was attributed to the change of growth mechanism due to the load variation, while the crack arrest during one block loading brought about the crack growth deceleration.

Fatigue Crack Growth Behavior of Ti-6Al-4V Alloy with Bimodal Microstructure under Constant and Non-stationary Variable Amplitude Load Sequences

Fatigue crack growth behavior under constant and non-stationary variable amplitude load sequences was investigated using compact tension i specimens of Ti-6Al-4V alloy with bimodal microstructure. Fatigue crack growth rate and macroscopic crack closure were measured by means of an unloading elastic compliance method. The da/dn-ΔKeff relationship under constant amplitude exhibited a trilinear form even in so-called Paris region corresponding to the change of growth mechanism from the intergranular fracture in the low ΔK region to the transgranular one in the high ΔK region. The fatigue crack growth rate under two-step block loading was found to be higher than that estimated by da/dn-ΔKeff relation under constant amplitude loading, indicating that the load variation resulted in the crack growth acceleration terms of ΔKeff. The load variation induced the transgranular fracture in the low level loading where the intergranular fracture type was dominant under constant amplitude loading. It is considered that the transition of fracture type in the low level loading resulted in the acceleration. Under single over loading, however, the crack growth deceleration in terms of ΔKeff was observed due to the blunted crack tip.

Ｓｉ３Ｎ４‐ＢＮ複合焼結セラミックスの疲労き裂進展挙動に及ぼすＢＮ含有量および荷重変動の影響

In order to investigate effects of BN content and load variation on the fatigue crack growth behavior of Si3N4-BN composite ceramics (SNB), fatigue crack growth tests under constant amplitude loading and repeated two-step load sequences were carried out using compact type (CT) specimens. Crack length and macroscopic crack closure were measured using the unloading elastic compliance method. The maximum stress intensity factor for the same fatigue crack growth rate decreases with the increase of the BN content. This decrease with the increase of the BN content is resulted from the decline of the fracture toughness. Fatigue crack growth rate strongly depends on the maximum stress intensity factor, and is also influenced by the load amplitude. As for the load amplitude dependency of the crack growth rate, SNB40 is the most remarkable in comparison with SNB20 and SNB30. Regardless of the BN content, fatigue crack growth rate under repeated two-step loading was found to be accelerated in comparison with that under constant amplitude loading. The acceleration was due to the breaking of interlocking under high level loading. The acceleration of the crack growth rate of SNB40 is the most remarkable because the crack growth rate of SNB40 is strongly dependent on the load amplitude. The fatigue crack growth acceleration behavior under repeated two-step loading could not be explained by the equivalent stress intensity factor range ΔKeq in consideration of both of Kmax and ΔK. However, the equivalent effective stress intensity factor range ΔKeff, eq in consideration of both of Kmax and ΔKeff could account for the acceleration behavior qualitatively but not quantitatively.

レール鋼の疲労き裂進展特性に及ぼす累積通過トン数の影響

Influence of accumulative passing tonnage on fatigue crack growth in rail steels was investigated. The fatigue crack growth was measured using compact tension specimens cut from three kinds of rails with accumulative passing tonnage of 100MGT, 200MGT, 600MGT respectively. The fatigue crack growth rate was estimated by the effective stress intensity range ΔKeff obtained by an unloading elastic compliance method. In addition, the measurements of crack opening displacement and the analysis of fatigue fracture surfaces were carried out to clarify the mechanism of crack closure behavior by a scanning electron microscope. It was concluded that the roughness of fatigue crack surface dependent on the grain size of each rail steel influences the crack growth behavior, and that the influence of accumulative passing tonnage on fatigue crack growth behavior can be estimated by the threshold effective stress intensity range ΔKeff, th.

209 等軸α/針状α混合組織 Ti-6Al-4V 合金の変動荷重下における疲労き裂進展挙動

Fatigue crack growth tests under variable amplitude load sequences were carried out using compact tension specimens of Ti-6Al 4V alloy. Fatigue crack growth rate and macroscopic crack closure were measured by means of an unloading elastic compliance method. The effect of frequency and overload ratio on fatigue crack growth rates were discussed in terms of effective stress intensity factor range, ΔK_<eff>.

806 窒化けい素における 2 段繰返し変動荷重下の疲労き裂進展挙動に及ぼす頻度比の影響

In order to investigate effects of frequency ratio on fatigue crack growth behavior in a gas-pressure sintered silicon nitride, fatigue crack growth tests under two kinds of repeated two-step loading were carried out using compact tension specimens. Fatigue crack growth rate and macroscopic crack closure were measured by means of the unloading elastic compliance method. Crack growth rate at low level loading, (da/dn)L, was found to be accelerated in comparison with that under constant amplitude loading having same ΔK value. Effect of frequency ratio on crack growth behavior under repeated two-step loading holding K_<min> constant is remarkable, but under repeated two-step loading holding K_<max> constant is small.

Fatigue Crack Growth Behavior in Silicon Nitride under Constant and Variable Amplitude Load Sequences

In order to investigate cyclic fatigue crack growth behavior of a gas-pressure-sintered silicon nitride under constant and variable amplitude load sequences, fatigue crack growth tests were carried out using compact type (CT) specimens. The crack length and macroscopic crack closure were measured using an unloading elastic compliance method. Grain interlocking was observed around crack wake in all fatigue test conditions, which implied fatigue crack growth of this material was associated with progressive degradation of the grain interlocking by cyclic loading. The fatigue crack growth rate, da/dn, under constant amplitude loading was controlled not only by the maximum stress intensity factor, Kmax, but also the stress amplitude, while Kmax was the most important factor in cyclic fatigue crack growth. The overload and high-level load excursion produced the acceleration of fatigue crack growth and the downward shift of crack closure point under low-level loading. This decrease was thought to result from much severer crash or frictional wear of grain interlocking and the crack closure could explain the acceleration behavior qualitatively.

Automated real-time measurements of fatigue crack length and crack opening load using unloading elastic compliance method

A system has been developed to measure crack length and crack opening load automatically in real time without changing any testing condition, by using an unloading elastic compliance method. The crack opening load is determined by a unique method using differential displacement signal data. The performance of the developed system was verified through constant-amplitude crack growth testing. The system is a very simple system, composed of a personal computer, an analogue electrical subtraction circuit, a stepping motor, a stepping motor driver, a PIO board and applications software. This system is expected to be utilized for measurements of crack length and crack opening load under random loading, short crack growth studies and effective stress intensity factor range Δ K eff-controlled tests.

窒化けい素における一定および非定常変動振幅荷重下の疲労き裂進展挙動

In order to investigate the effect of load variation on the cyclic fatigue crack growth behavior of gas-pressure-sintered silicon nitride, fatigue crack growth tests under constant amplitude loading, multiple peak overloading, Lo-Hi and Hi-Lo two-step loadings were carried out using compact type (CT) specimens. Crack length and macroscopic crack closure were measured using the unloading elastic compliance method. Grain interlocking was observed around crack wake in all fatigue test specimens by SEM. Fatigue crack growth rate, da/dn, under constant amplitude loading was controlled by not only maximum stress intensity factor, Kmax, but also load amplitude. Crack opening stress intensity factor, Kop, decreased as load amplitude increased, as was concerned with breaking of grain interlocking. Overload caused the acceleration of fatigue crack growth rate, which was in contrast to the retardation observed in metallic materials. The acceleration was due to the breaking of grain interlocking by overload. The crack growth rate recovered as crack grew in a relatively short distance after overload, because grain interlocking in crack wake was reconstructed during crack growth.

窒化けい素の２段繰返し変動荷重下における疲労き裂進展挙動

In order to investigate the cyclic fatigue crack growth behavior of a gas-pressure-sintered silicon nitride under repeated two-step loadings, fatigue crack growth tests were carried out using compact type (CT) specimens. Crack length and macroscopic crack closure were measured using the unloading elastic compliance method. Regardless of repeated two-step loading patterns, the acceleration of fatigue crack growth rate was observed. High-level load execution was found to crash grain interlocking more severely and result in decrease of crack opening stress intensity factor, Kop, under low-level loadings. The fatigue crack growth acceleration behavior under repeated two-step loadings, where maximum load was kept constant, could be explained by crack closure behavior measured by the macroscopic method. However, under repeated two-step loadings where minimum load was kept constant, macroscopic crack closure behavior could account for the acceleration behavior qualitatively but not quantitatively.