Dynamic J-R curves and tension-impact properties of AISI 308 stainless steel weld

In this paper, instrumented tension-impact (dynamic tensile) and instrumented Charpy impact test results for AISI 308 stainless steel welds at room temperature are reported. A few Charpy specimens precracked to a/W (crack length to width ratio) ratios of 0.42 to 0.59 were also tested. Dynamic yield strength obtained from tension-impact test agrees well with that from Charpy V-notch specimens. The strain rates obtained during the tension-impact test are compared with the various estimates of strain rates for V-notch and precracked Charpy specimens. A variation of the compliance changing rate method was necessary for determining the crack initiation point while crack growth was determined by power law key-curve procedure. J-R curves thus obtained from Charpy (precracked and V-notch) specimens are compared with those computed using handbook procedures using dynamic tensile results. Key words: Tension-impact testing, 308 stainless steel weld, Charpy V-notch, dynamic fracture toughness, dynamic yield strength, J-R curve, strain rate, key-curve.     

Measurement of Specific Fracture Energy and Surface Tension of Brittle Materials in Powder Form

Studies of the influence of specimen geometry and size–effect on the K _R –curves and the related fracture parameters were carried out by the authors (Kumar and Barai 2008b). The present paper is a supplementary contribution and reports interesting results related to the effect of the loading condition and size–effect studies on the K _R –curves associated with the cohesive stress distribution for complete fracture process, the double–K fracture parameters, the CTOD–curves and the process zone length using two different loading conditions (i.e., three–point bending test and four–point bending test). The laboratory size specimen with initial–notch length/depth ratios 0.3 and 0.5 are considered in the work. The load–crack opening displacement curves for these loading conditions are obtained using well known version of fictitious crack model.     

Prediction of fatigue limit reliability of high strength steel with deep notch under mean stress <Emphasis Type="Italic">σ</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> = 0

Because a fatigue limit of high strength steel with Vickers hardness H _V > 400 is scattered, it is difficult to predict the fatigue limit for S-N curve experimentally. The authors have proposed a nondestructive method for predicting the fatigue limit reliability of plain specimen of the high strength steel by the stress-strength model which consists of “statistical characteristics of hardness of a matrix under a small indentation load” and “statistical characteristics of hardness required for non-propagations of fatigue cracks from microstructural defects in a material”. In this paper, a nondestructive method for predicting the fatigue limit reliability of notched specimen of the high strength steel with microstructural defects such as non-metallic inclusions and pits from characteristics of a stress field near a notch, statistical characteristics of Vickers hardness and defect size is proposed. Especially, the method is applied to a structure with a deep notch under a mean stress σ _m = 0. Then, fatigue tests were carried out on the notched specimens of quenched-tempered 0.5% carbon steels with H _V ≃ 600 changing a notch root radius under a constant notch depth, and the validity of the prediction method is examined by comparing predicted results to experimental ones.     

Effect of specimen size in determining ductile to brittle transition temperature

Ductile to brittle transition temperature (DBTT) for 9Cr–1Mo steel has been determined from Charpy impact testing for full size and subsized specimens. DBTT was obtained at various percentage of upper shelf energy (USE). Assuming that most of the energy is spent in crack initiation, notch root volumes of subsized specimens (V_NS) were normalised with full size specimen (V_NF), and a power law relationship between DBTT and notch root volume has been established. From finite element method, it is observed that the sum of von Mises stress (σ_eq) and hydrostatic stress (σ_h) reaches ～2400 MPa (fracture stress, σ_f*) as the specimen dimension decreases at a temperature corresponding to 33% USE. This corresponds to ～68 J of full size specimen used in the determination of nil ductility transition temperature.     

J-integral estimation for single edge notch specimens in tension

A new J-integral estimation scheme for single edge notch specimens in tension (SENT) is presented. The scheme consists of equations obtained by analysing finite element results of SENT specimens under plane strain conditions, and separate equations have been derived for two forms of idealized material stress-strain curves-power law and bilinear representations. Non-dimensional J values are presented as functions of non-dimensional far field strains which eliminate the dependency of J on the aspect ratios of specimens. It was found that both the material law and the crack depth to specimen depth ratio had significant influences on the predicted J values and by presenting equations for different parts of the J versus strain curves, the scheme is able to take these influences into account.     

Fatigue of shot peened 7075-T7351 SENB specimen – A 3-D analysis

As‐received or shot peened 7075‐T7351 single‐edged notch bend (SENB) specimens, 8.1‐mm thick, were fatigued at a constant maximum load and at stress ratios of R= 0.1 and 0.8 to predetermined numbers of fatigue cycles or to failure. The SENB specimens were then fractured by overload and the tunnelling crack profiles were recorded. The crack‐growth rate, da/dN, after crack initiation at the notch was determined by crack‐profile measurement and fractography at various fatigue cycles. The shot peened surface topography and roughness was also evaluated by three‐dimensional (3‐D) laser scanning microscopy. Residual stresses in the as‐received specimens and those generated by shot peening at Almen scales of 0.004A, 0.008A, 0.012A and 0.016A, were measured by an X‐ray diffraction stress analyser with an X‐ray target, CrK, every 0.1 mm to a depth of 1 mm. The 3‐D stress intensity factor of the curved crack front was determined by the superposition of the 3‐D finite element solutions of the stress intensity factor of the loaded SENB specimen without the residual stress and the stress intensity factor of the unloaded SENB specimen with a prescribed residual stress distribution. da/dN versus the resultant stress intensity factor amplitude, ΔK_I, plots showed that while the residual stress locally retarded the crack‐growth rate it had no effect on the overall crack‐propagation rate.     

Influence of specimen geometry and size-effect on the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">R</Emphasis></Subscript>-curve based on the cohesive stress in concrete

Comparative study for determining the K _R -curves associated with the cohesive stress distribution for complete fracture process for two standard specimen geometries i.e., three-point bending test and compact tension test specimen geometries of concrete using analytical method and weight function approach is reported in the paper. The laboratory size specimen (100 ≤  D  ≤  400 mm) with initial-notch length/depth ratios 0.3 and 0.5 are considered in the investigation. The load-crack opening displacement curves for these specimens are obtained using well known version of Fictitious Crack Model (FCM). It is found from the numerical results that the weight function method improves computational efficiency without any appreciable error. The stability analysis on the K _R -curves and the influence of specimen geometry and the size-effect on the K _R -curves, the CTOD-curves and the process zone length during crack propagation of complete fracture process are also described.     

Analytical evaluation of J-integral for elliptical and parabolic notches under mode I and mode II loading

In the present work the J-integral (indicated here as J_Vρ because two parallel flanks are not present) was calculated by using, along the free border, the exact analytical stress distribution for the ellipse and the asymptotic one for parabolic notches. The material was assumed as homogeneous isotropic and linear elastic. First, for an ellipse under remote tensile loading, the expression of J_Vρ has been analytically calculated on the basis of Inglis’ equations. The equations have been used to prove that, in terms of J-integral, the crack is the limit case of an equivalent elliptic notch. Furthermore, by distinguishing the symmetric and skew-symmetric terms, the well-known Stress Intensity Factors (SIF) of mode I and II for a crack in a wide plate under tension are obtained by adding a limiting condition. Second, by means of Creager–Paris’ equations, J_Vρ has been analytically calculated for a parabolic notch of assigned tip notch radius ρ. The asymptotic value of J_Vρ and the relationship between the peak stress and the relative SIF are the same as the ellipse. Finally, as an engineering application, we provide an accurate formula for the evaluation of the Notch Stress Intensity Factors of a crack, mainly subjected to tensile stress, from the peak stress of the equivalent ellipse under the same loading.     

A direct estimate of JIc from the load versus load-line displacement record

The purpose of this study is to examine the current standard fracture toughness test procedure to determine if there could be an easier method to get a J_Ic value from the test record. The current method for determining J_Ic involves a detailed computational and construction procedure. The objective in this study is to simplify the analysis for the determination of J_Ic. The results of this study show that the load and displacement record for a fracture toughness test can be used to directly estimate a J_Q value, a provisional value for fracture toughness, J_Ic. The J value taken at the maximum load point can be used along with an adjustment factor to estimate a J_Q value. This J_Q estimate is close to the one obtained from the construction procedure of ASTM Standard E 1820. When a unit‐sized specimen is tested, that is, a specimen with a width of 50 mm and a thickness of 25 mm the maximum load point provides a direct estimate of J_Q. Other sizes require a size adjustment factor, which is simply a square root relationship between the width of the test specimen and a unit width. The proposed new method of estimating J_Q is simple in concept and requires a minimum number of calculations. It appears to produce values of J_Q which are comparable to those obtained from the ASTM E1820 construction procedure and may produce less scatter.     

Dauerfestigkeit und Kerbempfindlichkeit der Legierungen AlMgSi1, AlCuMg2 und AlZnMgCu1,5

The Fatigue Strength and Notch Sensitivity of Al-Alloys 6061, 2024 and 7075. Comparison of the fatigue limits and fatigue notch factors for internally-notched sheet specimens of 6061-T4, 2024-T3-Alclad and 7075-T6-Alclad with k_T = 2 to 4,6. Effect of clad on the fatigue strength of notched specimens. Notch sensitivity k_F/k_T as a function of notch radius. Notch sensitivity of the investigated Al-alloys for various stress concentration factors k_T and stress ratios. Calculation of the fatigue notch factors of the investigated alloys with the aid of a two-parameter formula.     

The fatigue properties of cross-plied boron 6061 aluminium

The mechanical properties of 0/90° and 0/90/+-45° boron-aluminium laminates have been examined at room temperature, 200 and 300° C. The increase in test temperature resulted in decreases in both the tensile and fatigue properties. Relatively constant critical stress intensity values were obtained from centre-notched static tensile specimens, indicating high notch sensitivity. Smaller values were obtained from specimens tested at elevated temperatures.The tension-compression (R=–1) fatigue behaviour of unnotched specimens cut from either material indicated 10⁷ cycle endurance limits of about 255 MPa (37×10³psi) and endurance ratios of 0.3 to 0.4. Microscopic examination of failed specimens detected the presence of off-axis fibre splitting and multiple cracks that were distributed throughout the matrix. Fractographic observations indicated that the fatigue crack had propagated completely through the matrix before final failure of the fibres occurred.Notched specimens failed by fracture at the fatigue extended notch at approximately the same values of the critical stress intensity that had been determined statically. However, fatigue lives obtained from centre-notched specimens subjected to identical net section stresses indicated that the rate of propagation of the premachined notch was faster for specimens containing longer crack sizes only for crack length: specimen width ratios, 2a/w, up to 0.4; thereafter, larger ratios yielded slower crack propagation rates.     

The effect of notch geometry on critical distance high cycle fatigue predictions

A critical distance method for predicting the fatigue limit stresses of notched specimens was implemented for notched specimens with a wide range of notch dimensions. Circumferentially notched cylindrical specimens (k_t=1.97–4.07) taken from Ti–6Al–4V forged plate were cycled to failure (R=0.1 and 0.5) using a step loading method for estimating the 10⁶ cycle fatigue limit stresses. These experimental data were used in combination with finite element solutions for all specimen geometries to determine a ‘critical distance’, a quantity or parameter determined from the stress distribution surrounding the notch in combination with fatigue limit stress data from unnotched specimens. A unique parameter was not found for all of the specimen geometries. However, predictions for the fatigue limit stresses of the larger notch geometries may be made with some amount of accuracy using a single value of the critical distance parameter, while reasonable predictions for the specimens with the smallest notch dimensions may be made upon the recognition of an apparent size effect.     

Effect of fracture path on the toughness of weld metal

The crack propagation direction may affect weld metal fracture behavior. This fracture behavior has been investigated using two sets of single edge notched bend (SENB) specimens; one with a crack propagating in the welding direction (B×2B) and the other with a crack propagating from the top in the root direction (B×B) of a welded joint. Two different weld metals were used, one with low and one with high toughness values. For Weld Metal A, two specimen types have been used (B×B and B×2B) both with deep cracks. The weld metal A (with high toughness values) has reasonably uniform properties between weld root and cap. The resulting J-R curves show little effect of the specimen type, are ductile to the extent that the toughness exceeds the maximum J_max, value allowed by validity limits and testing is in the large –scale yielding regime. In the case of weld metal B (with low toughness values) with two specimen types (B×B and B×2B) the B×B specimen has shallow cracks while the B×2B specimen has deep cracks. Both resulting J-R curves show unstable behavior despite the fact that the types of specimen and their constraints are different. The analysis has shown that crack propagation direction is most influential for a weldment with low toughness in the small scale yielding regime, whereas its influence diminishes due to ductile tearing during stable crack growth and large scale yielding. The results have shown that these effects are different in both the crack initiation phase and during stable crack growth, indicating a dependence on weld metal toughness and the microstructure of the weld metal. It can be concluded that, if resistance curves during stable crack growth do not show differences in both notch orientations, the fracture toughness values of the whole weld metal can be treated as uniform.     

Plane elastostatic analysis of V-notched plates

Solutions are given for several plane elastostatic problems of plates having a V-notch on one edge, and subjected to a variety of boundary conditions. The effect of the magnitude of the V-notch angle and specimen geometry on stress intensity factors K _I and K _II are obtained for unloaded notch surfaces. There is less than one percent difference in opening mode I stress intensity factor in going from a zero degree notch angle to a 30 degree notch angle. Notch opening displacements at the plate edge were measured experimentally and the results obtained were in excellent agreement with the computed results.     

The fracture of boron fibre-reinforced 6061 aluminium alloy

The fracture of 6061 aluminium alloy reinforced with unidirectional and cross-plied 0/90°, 0/90/±45° boron fibres has been investigated. The results have been described in terms of a critical stress intensity,K _Q. Critical stress intensity factors were obtained by substituting the failure stress and the initial crack length into the appropriate expression forK _Q. Values were obtained that depended on the dimensions of the specimens. It was therefore concluded that, for the size of specimen tested, the values of the critical stress intensity,K _Q, did not reflect any basic materials property.     

A simplified method for determining double-K fracture parameters for three-point bending tests

A simplified method for determining the double-K fracture parameters K _Ic ⁱⁿⁱ and K _Ic ^un for three-point bending tests is proposed. Two empirical formulae are used to describe the crack mouth opening displacement CMOD and the stress intensity factor K _I ^c caused by the cohesive force (x) on the fictitious crack zone for three-point bending beams. It has been found that the two empirical formulae are accurate for a large practical region of a/D. Experiments carried out by many researchers showed that the new formula of CMOD for three-point bending beams can be directly used to predict the initial crack length for precracked beams, the notch depth and the critical effective crack length, as well as the crack length in the post-critical situation with a satisfactory accuracy. Further verification is demonstrated to determine the double-K parameters K _Ic ⁱⁿⁱ and K _Ic ^un. They are very close to those determined by the method proposed in our previous work. Using the simplified procedure, the experiments can be performed even without a closed-loop testing facility and the calculation can be carried out on a pocket calculator.     

Double crack problem in nonlocal elasticity

The singular stress field around a sharp notch tip is expressed as a sum of two independent fields: a symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaigdaaeqaaaaaaaa!3CC3!\[1/r^{1 - \lambda _1 } \]and a skew-symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaikdaaeqaaaaaaaa!3CC4!\[1/r^{1 - \lambda _2 } \]. The intensities of the symmetric and skew-symmetric singular stress fields are defined in terms of constants K _I and K _II, respectively. In this study, a plane problem of a strip with single or double edge notches under tension or in-plane bending is considered. The bisector of the notch may be inclined to the edge, so that the two singular stress fields with different singularities may be created simultaneously at the notch tip. The body force method is used to calculate the stress intensity factors K _I and K _II. In numerical analysis, basic density functions of the body forces are introduced to characterize the stress singularity at the notch tip. The advantages of this technique are the high accuracy of results, due to the smoothness of the unknown weight functions, and the presence of the direct relation between the values of K _I and K _II and the values of unknown weight functions. The stress intensity factors are systematically calculated for the various geometrical conditions.     

Stress concentration formulae useful for any shape of notch in a round test specimen under tension and under bending

In this work stress concentration factors, K_t , for a round bar with a circular-arc or V-shaped notch are considered on the basis of exact solutions for special cases and accurate numerical results. Then, a set of K_t formulae useful for any shape of notch is proposed. The conclusions can be summarized as follows. (i) For the limiting cases of deep (d) and shallow (s) notches, the body force method is used to calculate the K_t values. Then, the formulae are obtained as K_td and K_ts . (ii) On the one hand, upon comparison of K_t and K_td it is found that K_t is nearly equal to K_td if the notch is deep or blunt. (iii) On the other hand, if the notch is sharp or shallow, K_t is mainly controlled by K_ts and the notch depth. (iv) The notch shape is classified into several groups according to the notch radius and notch depth. Then, the least-squares method is applied for the calculation of K_t /K_td and K_t /K_ts . (v) Finally, a set of convenient formulae is proposed that are useful for any shape of notch in a round test specimen. The formulae give SCFs with <1% error for any shape of notch.     

Fatigue life prediction of small notched Ti-6Al-4V specimens using critical distance

This study investigated the method of estimating the fatigue strength of small notched Ti-6Al-4V specimen using the theory of critical distance that employs the stress distribution in the vicinity of the notch root. Circumferential-notched round-bar fatigue tests were conducted to quantify the effects of notch radius and notch depth on fatigue strength. The fatigue tests show that the larger notch radius increases the fatigue strength and the greater notch depth decreases the fatigue strength. The theory of critical distance assumes that fatigue damage can be correctly estimated only if the entire stress field damaging the fatigue fracture process zone is taken into account. Critical distance stress is defined as the average stress within the critical distance from notch root. The region from the notch root to the critical distance corresponds to the fatigue fracture process zone for crack initiation. It has been found that a good correlation exists between the critical distance stress and crack initiation life of small notched specimens if the critical distance is calibrated by the two notched fatigue failure curves of different notch root radii. The calibrated critical distances did not vary clearly over a wide range of fatigue failure cycles from medium-cycle low-cycle fatigue regime to high-cycle fatigue regime and have an almost constant value. This critical distance corresponds to the size of crystallographic facet at the fatigue crack initiation site for the wide range of fatigue cycles.     

Magnetovoltage Measurements and Hysteresis Effects in Polycrystalline Superconducting Y1Ba2Cu3O7−x /Ag in Weak Magnetic Fields

The magnetovoltage measurements (V–H curves) with different sweeping rates (dH/dt) of the external magnetic field in Ag-added polycrystalline YBa₂Cu₃O_7?x sample (YBCO/Ag) were investigated. The measurements of V–H curves were carried out as functions of the transport current (I) and temperature (T). Upon cycling H, all V–H curves measured for different values of I exhibit a clockwise hysteresis effects in forward region. The hysteresis effects in the V–H curve were interpreted in terms of two-level magnetic system, which considers the superposition of the external magnetic field and the local magnetic fields in the intergrain boundaries induced by magnetic dipole moment of neighbor superconducting grains. The analysis of magnetovoltage data showed that the flux trapping in the junction network has a negligible effect on the evolution of the V–H curves and the irreversibilities arise mainly from the flux trapping inside the grains. It is shown that the width of V–H curves shows a universal scaling behavior with respect to the applied current below the critical temperature T _c . The comparison of V–H curves of the YBCO/Ag sample with those of YBCO shows that adding Ag to the superconducting structure weakens the pinning properties of Josephson medium and provokes the instabilities in measured dissipation. The presence of Ag in the superconducting matrix causes marked decrease in hysteresis effects and makes the V–H curves dH/dt dependent. At high values of dH/dt, the instabilities and plateau regions in V–H curves increase significantly as compared to those of observed in YBCO. In addition, the interrelation between the evolution of V–H curves obtained for different values of I and the critical current I _c was demonstrated experimentally.