Stress-intensity factors of hollow notched bars and hydrogen-embrittled specimens

Results of an experimental program for determining stress-intensity factors utilizing round tensile specimens are presented. Hydrogen embrittlement was utilized as a crack starter for several solid specimens. Notched hollow rounds of various geometries were tested and evaluated.     

Buckling of an elastoplastic bar

Buckling of a bar of an elastoplastic material is studied. It is shown that for any (σ-?) diagram of the bar material, the limit load (the longitudinal external force) in dimensionless variables that the bar can withstand does not exceed the current bending stiffness of the most loaded (in terms of the bending moment) section.     

Embedded-strain-sensor development for composite smart structures

The winding or layup procedure for fiber-reinforced composites lends itself to convenient installation of embedded sensors during fabrication. These permanently installed and protected sensors could be used during the service lifetime of the structure to monitor real-time conditions and determine when loading or vibration is excessive, and when damage has occurred. Such ‘smart or intelligent’ structures could be used to provide continuous ‘health monitoring’ of the structure as well as provide input for active vibration control. In the present study, two sizes of constantan wire (0.15-mm and 0.025-mm diameter) with a very thin but tough polyimide insulation were embedded in graphite-epoxy bars and tubes. The 25-mm by 2.5-mm by approximately 300-mm long bars were fabricated from hand-laid-up panels and subjected to static four-point bending and cantilever bending. The tubes (42-mm diameter by 1.25-m long) were subjected to static cantilever bending. Output from the constantan wire was monitored with conventional strain-gage indicators. Results indicate accurate tensile and compressive measurements of the integrated strain along the length of the constantan wire when compared with beam formulas and surface mounted strain gages. The constantan strain wire shows promise as an embedded sensor for ‘smart structures’.     

Determination of Weibull's parameters on flexure strength of round beams of aluminum-copper alloy and cast iron

Weibull's parameters for the three-point bending of a round bar specimen made of aluminum-copper alloy and cast iron, both white and grey, are obtained to predict the cumulative probability of fracture. Unlike the rectangular beam specimens which are more sensitive to changes in the boundary conditions, results for the round bar specimens are better behaved and expressed in terms of the cumulative probabilities of fracture. Specimen size effects were overshadowed by variations in the material properties caused by unequal cooling rates and inhomogeneities in the material microstructure.     

Crack-stability analysis and fracture toughness of ceramic bend bars with a modified circular cross section

Previous analysis has shown that the round bend bar is more stable than the rectangular bend beam. The geometry of the round bend bar was slightly modified to permit precracking of ceramic bars for subsequent fracture-toughness testing. Stability solutions of this new modified round bend bar were found as a function of precrack length for several machine-compliance values. A threshold crack length was determined which predicted the transition from unstable to stable fracture behavior. Experiments with silicon nitride and alumina specimens verified the results of the analysis.     

Stress-intensity factor for plain concrete in bending—Prenotched versus precracked beams

A series of experiments conducted to compare the behavior of beams with notches to those with natural cracks has recently been completed. A total of 42 beams with notches formed by casting teflon strips into the concrete were tested to failure. A companion series of 42 beams were statically precracked following the procedure described in Ref. 5. The ranges of crack depth to beam depth varied from 0.3 to 0.7 (nominally). Two strengths of concrete were used and the 3-in.×4-in.×15-in. (span) beams were tested on three-point or four-point bending. Comparisons are made on the basis of computed stress intensity using a finite-element program developed by the writers. Results of this study show the following: (1) in all cases the naturally cracked beams yielded higher failure loads and stress-intensity values than notched beams with the same crack length; (2) the averageK ₁ values for precracked beams were approximately 38 percent, 77 percent and 96 percent greater than for notched beams for crack-depth ratios of 0.3, 0.5 and 0.7 respectively.     

A new fracture-toughness test method for thick-walled cylinder material

A new method for measuring the plane-strain fracture toughness of the material from a thick-walled cylinder is presented. This method utilizes a notched, “C”-shaped test specimen, pin loaded in tension. This specimen has the advantage of most efficiently utilizing the available material to obtain the maximum possible triaxial constraint at the crack tip. Stress-intensity-factor calibrations for this specimen were obtained by two independent experiments. These are a compliance test, as originally proposed by Irwin, and a fatigue-crack-growth test, as suggested by James and Anderson. Very good agreement was obtained between the results of these two experiments. A stress-intensity calibration for a similar geometry was also obtained using a finite-element analysis and a method developed by Kobayashi to determine stress-intensity factors from finite-element results. The results of this method appear to be low by about 10 percent. Comparative fracture-toughness tests of material from a 2-in.-thick plate of special aircraft quality, 4340 steel, were conducted using the proposed new test method and the ASTM standard bend specimen. These results agreed within 2 percent.     

Stresses in turbine-blade tenons subjected to bending

The photoelastic method was used to model large steam turbine tenon-shroud attachments under bending loads. Six models were used to investigate three basic tenon geometries: (a) single round tenon—here two different fillet radius-to-tenon diameter ratios were examined; (b) long narrow tenon—for this geometry the influence of shroud-seating clearance and shroud stiffness was investigated; (c) two separated round tenons. Stress-concentration factors for the tenon fillets were determined based on the nominal bending stress in the tenon using the moment of inertia of the tenon cross section. For the single round tenon, stress-concentration factors of 1.3 and 1.6 were found for fillet radius-to-tenon diameter ratios of 0.41 and 0.19. These compared very well with those values obtained by treating the geometry as a stepped round bar with a shoulder fillet subjected to bending. The long-narrow-tenon geometry showed a higher stress-concentration factor than the two separated round tenons—6.1 compared to 2.9. Increasing the shroud stiffness reduced the stress-concentration factor for the long-narrow-tenon design.     

Fracture-toughness tests and displacement and crack-stability analyses of tungsten round bend specimens

Plane-strain fracture-toughness tests were performed using the recently proposed round-bar bend test procedure with a liquid-phase sintered tungsten alloy. The tests included a direct comparison of fracture toughness from rectangular and round-bend specimens and measurements of load-line compliance using the unloading technique ofJ-integral fracture tests. Complementary displacement and crack-growth stability analyses of the round bar were performed as an extension of recent work in these two areas.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM.     

An experimental weight function for stress-intensity-factor calibrations

This paper describes a set of experiments conducted to demonstrate application of weight-function methods to experimental stress-intensity-factor calibrations. The weight-function method allows stress-intensity-factor and crack-surface-displacement information obtained for one loading to be generalized in a form which allows direct computation of stress-intensity factors for other load configurations applied to the crack geometry under consideration. The specific results described here demonstrate that experiments with edgecracked strips loaded in four-point bending also provide stress-intensity factors for remote lension and three-point bend-load applications.     

Photoelastic investigation on the crack-arrest capability of a hole

Dynamic photoelasticity employing a 16-spark gap Cranz-Schardin camera system was used to determine certain conditions leading to fracture arrest by a circular hole ahead of a propagating crack. Photoelastic models of 3/8×10×10-in. Homalite-100 plates with a 1/2-in. edge crack were loaded in a fixed-grip configuration and crack arrest was made possible by central holes of 1/2, 1/4, and 0.15-in. diameters. In one test of a uniformly loaded plate with a central hole of 0.15-in. diameter, the propagating crack continued through this hole. Changes in dynamic-stress-intensity factors, as the crack tip approaches the hole, as well as changes in the dynamic-stress-concentration factors at the far side of the hole were studied, and these results were compared with the corresponding static results determined by finite-element analysis. This comparison shows that the static analysis can be used to qualitatively assess the arrest capability of the hole using the maximum static-stress concept or the proposed concept of strain energy released as the crack penetrates the hole.     

用光弹性法测定复合应力强度因子

工程结构裂纹尖端应力强度因子(SIF)由于形状、荷载的复杂性及边界条件的不确定性,难以用解析法得到,数值计算也有困难,而光弹性法弥补了上述方法的不足。本文用环氧树脂制作圆轴模型,采用机加工的方法制作圆轴模型裂纹,然后将加载模型进行应力冻结,通过光弹性实验研究分析了圆轴裂纹尖端应力分布。由于带环形裂纹的圆轴在弯扭组合变形时,离中性轴最远的裂纹尖端处于复合裂纹状态,而三维光弹性应力冻结法是测定复杂三维问题复合裂纹的有效方法。本文用双参数法测定I型应力强度因子,用切片逐次削去法测定Ⅲ型应力强度因子,实验误差较小。     

Beam subjected to eccentric longitudinal impact

This paper is concerned with an experimental investigation of the bending stresses in a bar subjected to eccentric longitudinal impact. The test beam was a round steel bar, 1 in. in diam and 8 ft long which was suspended by wires at two points. Strains were measured by SR-4 strain gages at 18 stations along the bar. The signals were fed through an amplifier to an oscilloscope and the trace on the screen was photographed for a permanent record. The impact was obtained by means of a striking bar with a conical end. The striking bar was suspended in a pendulum rig and striking height adjusted so as to impact the test bar at any desired eccentricity. The dimensionless impact durationt/T ₁ is about 0.02, whereT ₁ denotes the fundamental period of the beam. A theoretical analysis of the response of a free-free beam subjected to a dynamically applied end moment is undertaken to correlate analytical theories with the experimental results. The theoretical results based on the Timoshenko theory were found numerically, using the method of characteristics. Good agreement is found for the moment response curves at ten representative beam stations. Comparison is also made with related results from the Bernoulli-Euler theory, using the normalmode method. The numerical calculations were carried out on both IBM 704 and IBM 650 digital computers.     

Some analytical solutions for Saint-Venant torsion of non-homogeneous cylindrical bars

The Saint-Venant torsion problem of linearly elastic cylindrical bars with solid and hollow cross-section is treated. The shear modulus of the non-homogeneous bar is a given function of the Prandtl's stress function of considered cylindrical bar when its material is homogeneous. The solution of the torsional problem of non-homogeneous bar is expressed in terms of the torsional and Prandtl's stress functions of homogeneous bar having the same cross-section as the non-homogeneous bar.     

Determination of fracture toughness by photoelastic coating

The photoelastic-coating method was applied to the determination of fracture toughness in aluminum plates. The specimens were plates with a central transverse crack. Determinations were made first by the compliance method. The specimens were loaded statically to failure. The opening displacement across the crack was measured with a clip gage. In using this photoelastic-coating method, the stress-intensity factor was obtained in terms of the radius and fringe order of various isochromatic fringe loops using an extrapolation law. An apparent stress-intensity factor was obtained from several isochromatic fringe patterns away from the crack tip and then extrapolated to the crack tip to determine the true value. Results obtained by the photoelastic-coating method are higher than those obtained by the compliance method for all loads, due to the bluntness of the crack tip in the first set of specimens. Theoretical predictions fall between the compliance method and photoelastic-coating results. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

Optimal design of box-section sandwich beams in three-point bending

Minimum mass designs are obtained for box-section sandwich beams of various cross-sections in three-point bending. The overall compliance of the hollow, tubular beams are decomposed additively into a global contribution due to macroscopic bending (Timoshenko beam theory) and a local contribution associated with transverse deflection of the walls of the hollow beam adjacent to the central loading patch. The structural response is analysed for beams of square sections with various internal topologies: a solid section, a foam-filled tube with monolithic walls, a hollow tube with walls made from sandwich plates, and a hollow tube with walls reinforced by internal stiffeners. Finite element analysis is used to validate analytical models for the overall stiffness of the tubes in three-point bending. Minimum mass designs are obtained as a function of the overall stiffness, and the relative merits of the competing topologies are discussed.     

Scattered-light determination of mode I stress-intensity factors by a fringe gradient independent technique

Integration of the scattered-light stress-optic law and established bending and singular crack-tip relationships yielded new experimental equations for calibration and for the determination of mode I stress-intensity factors which are independent of a stress-fringe gradient. Scattered-light stressoptic coefficients determined from four-point bending tests and an integrated scattered-light bending equation show good agreement with values based on stress-fringe gradients computed with polynomials. Excellent agreement was also shown between mode I stress-intensity factors predicted by the integrated stress-optic equation and analytical solutions available in the literature. Favorable comparisons were also made with predictions based on a polynomial-finite-difference method of determining a stress-fringe gradient. Analyses were limited to flaw geometries and locations where there was minimal rotation of the refraction tensor.     

Some analytical solutions for Saint-Venant torsion of non-homogeneous anisotropic cylindrical bars

The Saint-Venant torsion of linearly elastic anisotropic cylindrical bars with solid and hollow cross-section is treated. The shear flexibility moduli of the non-homogeneous bar are given functions of the Prandtl's stress function of considered cylindrical bar when its material is homogeneous. The solution of the torsion problem of non-homogeneous anisotropic bar is expressed in terms of the torsion and Prandtl's stress functions of the corresponding homogeneous anisotropic bar having the same cross-section as the non-homogeneous bar.     

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved. The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poisson's ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions. The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.     

Comparison of Low Impedance Split-Hopkinson Pressure Bar Techniques in the Characterization of Polyurea

The split-Hopkinson pressure bar (SHPB) technique has been widely employed for over fifty years in characterizing the high strain-rate properties of many common engineering materials. Historically, however, this technique has had limited success in characterizing soft materials, since their low mechanical impedances can increase delays in attaining dynamic equilibrium and result in transmission pulses with extremely low signal-to-noise ratios. Due to interest in improving characterization of soft materials at high strain rates, numerous modifications to the traditional SHPB technique have been proposed. These include: using more sensitive piezoelectric gauges, employing hollow transmission bars, utilizing lower impedance polymeric pressure bars, and the use of pulse shaping techniques. To date, there has been no comparative studies or consensus within the SHPB community as to which approach is most advantageous. The goal of this investigation is to compare a number of these techniques, specifically the use of PMMA pressure bars and a hollow aluminum transmission bar (both with and without pulse shaping), alongside more traditional solid aluminum pressure bars in the characterization of polyurea, a common low impedance polymer. The advantages and disadvantages of each technique in generating high strain-rate stress-strain curves are discussed.