Photoelastic investigation on the Crack-arrest capability of a pretensioned stiffened plate

Dynamic photoelasticity, employing a 16-spark-gap Cranz-Schardin camera system, was used for dynamic analysis of propagating cracks in stiffened panels. The method of finite elements was used for a corresponding static analysis. Photoelastic models included 0.009525×0.25×0.25 m Homalite-100 plates with 10- and 25-percent pin-joined and bonded stringers. Static and dynamic strain-energy release rates, kinetic-energy release rates and stringer-load concentration factors were determined in stiffened panels that were pretensioned and then impacted by a projectile. It was found that the arrest capability of a stiffened panel could be assessed through the kinetic-energyrate concept. Also bonded stiffeners were found to be more effective in arresting a propagating crack than a corresponding pin-joined stiffened panel.     

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.     

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.     

Biaxial testing of [O2/±45] s graphite/epoxy plates with holes

An experimental investigation was conducted to study the behavior under biaxial-tensile loading of [O₂/±45] _s graphite/epoxy plates with circular holes and to determine the influence of hole diameter on failure. The specimens were 40-cm×40-cm (16-in.×16-in.) graphite/epoxy plates of [O₂/±45] _s layup. Four hole diameters, 2.54 cm (1.00 in.), 1.91 cm (0.75 in.), 1.27 cm (0.50 in.) and 0.64 cm (0.25 in.), were investigated. Deformations and strains were measured using strain gages and birefringent coatings. Biaxial tension in a 2∶1 ratio was applied by means of four whiffle-tree grip linkages and controlled with a servohydraulic system. Stress and strain redistributions occur around the hole at a stress level corresponding to localized failure around the 67.5-deg location and nonlinear strain response at the 0-deg location. Maximum measured strains at failure on the hole boundary are higher (approximately 0.016) than the highest ultimate strain of the unnotched laminate (0.010). Two basic patterns of failure were observed: (a) horizontal cracking initiating at points off the horizontal axis and accompanied by extensive delamination of the subsurface ±45 deg plies, and (b) vertical cracking along vertical tangents to the hole and accompanied by delamination of the outer 0-deg plies. The strength reduction ratios are lower than corresponding values for uniaxial loading by approximately 16 percent, although the stress-concentration factor under biaxial loading is lower.     

Experimentally determined stress-intensity factors for single-edge-crack round bars loaded in bending

Dimensionless stress-intensity factors were determined for single-edge-crack solid and hollow round bars loaded in bending. These factors were calculated from experimental compliance (inverse slope of load-displacement curve) measurements made on round bars loaded in three-point bending. The compliance specimens had span to diameter ratios of 6.67 and 3.33, and measurements were made over a range of dimensionless crack lengths from 0.002 to 0.70. The tests were made using 3-in. (76-mm) and 6-in. (152-mm) solid and hollow round bars notched on one side; the hollow bars had an inner to outer diameter ratio of 0.33. A comparison was made with data in the literature for rectangular bars; for ana/D of 0.0001, the dimensionless stress-intensity factor for a solid round bar is 1.3 vs. 2.0 for a rectangular bar.     

Static and dynamic analysis of the DCB problem in fracture mechanics

A finite difference scheme for treating the static and dynamic stress fields under plane-strain conditions in the DCB, is proposed. The adequacy of the scheme is established via the static solution by comparing the results obtained numerically with those obtained experimentally. Both the numerical and experimental results are also compared with data available in the literature. Discrepancies found are explained and discussed. For the numerical scheme adjusted to handle the propagating crack problem, the results represent a situation which is close to that observed experimentally; namely, an essentially constant steady state crack propagation speed from the start, with crack length at arrest and velocity values depending on the initial conditions. In addition, the velocities predicted by the analysis are shown to be in good agreement with those reported in the literature.     

Micromechanical fatigue testing

This paper describes the design, modeling, and experimental test results of a single crystal silicon micromechanical device developed to evaluate fracture and fatigue of silicon based micromechanical devices. The structure is a cantilever beam, 300 microns long, with a large silicon plate and gold inertial mass at the free end. Torquing and sensing electrodes extend over the plate, and with associated electronics, drive the structure at resonance. Fatigue crack propagation is measured by detecting the shift in the natural frequency caused by the extension of a preexisting crack introduced near the fixed end of the cantilever. Experimental data are presented demonstrating time-dependent crack growth in silicon. Crack extensions of 10 to 300 nm have been measured with a resolution of approximately 2.5 nm, and crack tip velocities as low as 2.1×10⁻¹⁴ m/s. It is postulated that static fatigue of the native surface silica layer is the mechanism for crack growth. The methodology established here is generic in concept, permitting sensitive measurement of crack growth in larger fatigue specimens as well.     

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.     

Strain energy density approach to stable crack extension under net section yielding of aircraft fuselage

In this paper, the incremental theory of plasticity is used in conjunction with the strain energy density criterion to determine the stress field in 4-in. wide test specimens containing 3 holes. These specimens, made from 0.04-in. thick sheets of 2024-T3 aluminum, also contained small collinear cracks emanating from the holes. The initial crack sizes varied from 0.15 to 0.26 in. Residual strength tests conducted with these specimens revealed that stable tearing occurred before failure. Analyses were performed to predict the stable crack extension and failure by plastic collapsed. Because of the complexities involved with nonlinear stress analysis combined with subcritical crack extension, the finite element method was used with the grid pattern adjusted for each increment of stable tearing. Reasonable correlation between the experimental data and predicted results was achieved.     

Dynamic stability of a propagating crack

In this work we investigate the stability of a straight two-dimensional dynamically propagating crack to small perturbation of its path. Willis and Movchan (J. Mech. Phys. Solids 43 (1995) 319; J. Mech. Phys. Solids 45 (1997) 591) constructed formulae for the perturbations of the stress intensity factors induced by a small three-dimensional dynamic perturbation of a nominally plane crack. Their solution is exploited here to derive equations for the in-plane and out-of-plane perturbations of the crack path making use of the Griffith fracture criterion and the principle of “local symmetry” (i.e the crack propagates so that local K_II=0). We consider a crack propagating in a body loaded by a pair of point body forces and subjected to a remote uniaxial stress, aligned with the direction of the unperturbed crack. We assume that the loading follows the crack as the crack advances and is such that the unperturbed crack is subjected to Mode I loading. We perform an analysis of the stability of the dynamic crack in a similar way as in earlier work (Obrezanova et al., J. Mech. Phys. Solids 50 (2002) 57) on the quasistatically advancing crack. We present numerical results illustrating the influence of the crack velocity on the crack stability. Numerical computations of the possible crack paths have been performed which show that at velocities of crack propagation exceeding about one-third of the speed of Rayleigh waves the crack may admit one or more oscillatory modes of instability.     

预置圆孔膨胀环动态断裂行为研究

利用中心线起爆膨胀环加载技术,采用分幅摄影技术观测了20号钢圆环在准一维拉伸作用下,预置圆孔缺陷临近区域的动态断裂特征。获得了高应变率下圆孔的变形、裂纹的萌生及扩展过程。并采用LS-DYNA3D有限元程序分步建模,将驱动器对膨胀环的冲击压力简化为直接作用于圆环内壁的压力历史,以此模拟了整个断裂过程。通过实验图像,得到裂纹尖端的位移以及速度随时间变化的曲线。结果表明,宏观可见裂纹出现于应力集中最大处,裂纹扩展速度随时间振荡,数值模拟与实验结果吻合较好。     

Evaluation Using Digital Image Correlation of Stress Intensity Factors in an Aerospace Panel

The fracture behavior of a crack propagating in a large (4.8 m × 1.4 m) aircraft panel was investigated quantitatively by experiment for the first time using digital image correlation. Mixed mode (I+II) stress intensity factors were evaluated using a methodology, which combined digital image correlation with the multi-point over-deterministic method to fit displacement field equations to the experimental data from around a crack tip. More than 800 images were taken during a 10-minute time period as the fracture of the panel occurred under monotonic loading. It was observed that the crack propagated through the skin of the panel at a relatively low speed, with an average crack tip velocity of 0.014 mm/s, and changed its propagation direction at particular points due to the reinforcement of the structure. In the later stages of the test, substantial shear lips were observed indicating a state of plane stress as would be expected in a thin, wide panel and the size of the plastic zone increased substantially. The value of the mode I stress intensity factor obtained from the measured displacement fields initially increased linearly to around 50 MPa√m (K_Ic = 37 MPa√m) and afterwards non-linearly reaching 300 to 400 MPa√m for crack extensions of the order of 100 mm. It is proposed that these high values of stress intensity factor do not represent an unrealistically high material fracture toughness but rather are indicative of the high resistance to crack growth of the structural assemblage of ribs, stringers and hole reinforcements in the panel which allow the skin to sustain a strain level that would otherwise cause unstable crack growth. Digital image correlation is demonstrated to be particularly powerful in elucidating this structural behavior.     

Elastoplastic near field solution for mode II crack loaded by remote shear stress in an infinite plate

A suitable elastic stress field near the crack line which satisfied the far field boundary conditions and the boundary conditions of the crack surfaces has been obtained and successful analysis has been made of a near crack line field for an infinite elastic-perfectly plastic medium containing a quasi-statically propagating plane stress crack subjected to far field shear stress. It is shown that the solutions of the problem of mode II crack loaded by remote shear stress from the Westergaard method in some previous papers is used as the elastic stress field near the crack line, are inappropriate.     

Strain measurements in tubes during rapid transient heating

A measuring apparatus using reluctance-type displacement transducers was successfully used for measuring radial thermal strains in 1-in.-diam × 8-in.-long thin-walled tubes of molybdenum, tantalum and 304 stainless steel. Wall-temperature rates of approximately 300° F/sec were accomplished by rapid heating with a plasma jet and strains at temperatures up to 2500° F were recorded. Excellent agreement between experimental results and a theoretical solution based on temperature profiles was found for temperatures to 2000° F.     

Numerical analysis of fast fracture and crack arrest in a sheet of elastic perfectly-plastic material

The dynamic fields for acceleration, deceleration and arrest of a crack tip have been investigated numerically. We consider cracks which start to extend rapidly under brittle conditions. The crack-tips then enter regions of elasto-plastic constitutive behavior and they are subsequently arrested. Results have been obtained for a symmetrically expanding central crack and for an edge crack, both in thin sheets. The elasto-plastic behavior has been described by J₂ flow theory, with the von Mises yield criterion and a bilinear relation between effective stress and effective strain. Numerical results are presented for stress and strain components at a short distance ahead of the propagating and arresting crack tips.     

Stress intensity factors for an arbitrarily oriented crack near a hole in longeron web

Damage-tolerant design of composite components in aerospace structures requires computationally effective stress and failure analysis methods. This study introduces an analytical/numerical method to determine the stress field and the stress intensity factors in a composite longeron web with an arbitrarily oriented straight crack near a hole. Typical of webs in wing longerons with massive belts, the tapered web is loaded in bending and shear. The solution method makes use of the complex potentials in conjunction with the boundary collocation technique. The present results are in close agreement with those obtained by finite element.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

Performance of Rubberized and Hybrid Rubberized Concrete Structures under Static and Impact Load Conditions

In this study, rubberized concrete samples were prepared by partial substitution (5 %, 10 % and 20 % replacements by volume) of sand by waste crumb rubber, and tested under impact three-point bending load, as well as static load. Three types of specimens (size 50?×?100?×?500 mm) namely, plain concrete, rubberized concrete, and double layer concrete (with rubberized concrete top and plain concrete bottom) were loaded to failure in a drop-weight impact machine by subjecting to 20 N weight from a height of 300 mm, and another three similar specimens were used for the static load test. In both the tests, the load–displacement and fracture energy of each specimen were investigated. Finite-element simulations were also performed to study the dynamic behaviors of the samples, by using LUSAS V.14 software. It was noticed that, the impact tup, and inertial and bending loads increased with the increase in the percentage of sand replacement by crumb rubber. It was interesting to observe that these effects were more significant in the double layer specimen compared to the plain and rubberized concrete samples. The static peak bending load always decreased with increase of rubber in the mix. In general, the strength and energy absorbing capability of rubberized concrete was better under impact loading than under static loading. The simulated load against displacement behaviors of all the samples were validated by the experimental results.     

Mixed Mode Dynamic Fracture in Particulate Reinforced Functionally Graded Materials

A detailed analytical and experimental investigation is presented to understand the dynamic fracture behavior of functionally graded materials (FGMs) under mode I and mixed mode loading conditions. Crack-tip stress, strain and displacement fields for a mixed mode crack propagating at an angle from the direction of property gradation were obtained through an asymptotic analysis coupled with a displacement potential approach. This was followed by a comprehensive series of experiments to gain further insight into the behavior of propagating cracks in FGMs. Dynamic photoelasticity coupled with high-speed photography was used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the FGMs. Dynamic fracture experiments were performed using different specimen geometries to develop a dynamic constitutive fracture relationship between the mode I dynamic stress intensity factor (K _ID ) and crack-tip velocity ( ) for FGMs with the crack moving in the direction of increasing fracture toughness. A similar -K _ID relation was also obtained for matrix material (polyester) for comparison purposes. The results obtained show that crack propagation velocities in FGMs were about 80% higher than the polyester matrix. Crack arrest toughness was found to be about 10% lower than the value of local fracture toughness in FGMs.     

Dynamic interaction effects of multiple delaminations in plates subject to cylindrical bending

The interaction of multiple delaminations in a laminated composite plate loaded dynamically under plane strain conditions (cylindrical bending) is studied by a simple but accurate model that represents the delaminated plate as a set of Timoshenko beams joined by cohesive interfaces. Behavioral maps are derived, which distinguish conditions under which multiple delaminations tend to propagate with equal lengths from those under which one of them tends to grow as a dominant crack with relatively high velocity. In homogeneous systems, equal length growth is favored when the delaminations are equally spaced through the thickness. While the behavioral maps are similar to those for static loading conditions, significant dynamic effects arise in the details of propagation: the maximum energy release rate depends strongly on the loading rate, duration and profile; dynamic effects and crack-interaction effects are generally coupled; and strong hammering effects (chaotic collisions of sub-laminates) can occur during the free wave motions that arise after the load is removed. The hammering effect can be suppressed by imposing a large-scale bridging mechanism (bridging extending far in the crack wake, as from pins or stitches), whereupon energy release rates tend to show smooth oscillations associated with waves propagating on the scale of the whole specimen. The energy absorbed during failure will depend significantly on whether conditions favor multiple delaminations propagating with equal lengths or a single delamination growing dominantly.