A photoelastic investigation of asymmetric four point bend shear test for composite materials

The asymmetric four point bend (AFPB) test, which utilizes a notched specimen and is a modification of the Iosipescu test, is investigated for measuring the shear stress fringe value of orthotropic birefringent model materials. The influence of the notch parameters, such as the notch angle and the notch radius, is first studied in the case of an isotropic model material; a notch angle of 120°, with or without a radius at the notch tip, lowers the shear stress concentration and leads to a better stress fringe value compared to a 90° notch. In the case of a unidirectionally reinforced glass-polyester model material, while the shear stress fringe values given by the 90°, 120°, sharp and radiused notches are reasonably close to the value obtained for an off-axis tensile specimen, no conclusions about the influence of the notch parameters can be drawn due to the peculiarities of the photoelastic response of the inhomogenous orthotropic model material. However, the failure modes indicate that a notch radius and the 120° notch angle reduce the stress concentration. Comparison is made with finite element results.     

Failure assessment of notched polycrystalline graphite under tensile-shear loading

The fracture load and the fracture initiation angle were experimentally measured for a V-notched specimen made of polycrystalline graphite under combined tensile-shear loading. The experimental results were obtained for several specimens with different notch angles and various notch tip radii. The experimental observations showed that for a constant notch tip radius, the fracture load in pure tensile loading conditions decreases as the notch angle increases. Moreover, for a constant notch angle, as the notch tip radius increases the fracture load in graphite specimens enhances in the entire domain between pure tensile and pure shear loading conditions. A recently developed failure criterion was then used to estimate the experimental values of the notch fracture resistance and the fracture initiation angle for the tested graphite specimens. The experimental results could be estimated very well by using the results of the proposed criterion.     

Size effect on buckling strength of eccentrically compressed column with fixed or propagating transverse crack

The strength and size effect of a slender eccentrically compressed column with a transverse pre-existing traction-free edge crack or notch is analyzed. Rice and Levy’s spring model is applied to simulate the effect of a crack or notch. An approximate, though accurate, formula is proposed for the buckling strength of the column of variable size. Depending on the eccentricity, the crack at maximum load can be fully opened, partially opened or closed. The size effects in these three situations are shown to be different. The exponent of the power-law for the large-size asymptotic behavior can be −1/2 or −1/4, depending on the relative eccentricity of the compression load. Whether the maximum load occurs at initiation of fracture growth, or only after a certain stable crack extension, is found to depend not only on the column geometry but also on its size. This means that the definition of positive or negative structural geometry (as a geometry for which the energy release rate at constant load increases or decreases with the crack length) cannot be extended to stability problems or geometrically nonlinear behavior. Comparison is made with a previous simplified solution by Okamura and coworkers. The analytical results show good agreement with the available experimental data.     

Notch effect on creep damage for Hastelloy C276-BNi2 brazing joint

The brazed structures have geometrical discontinuities like fillets working as notches. These notches have great effect on creep crack initiation and propagation. This paper studies the notch effect on creep damage for Hastelloy C276-BNi2 brazed joint, and the effects of notch type, notch radius and notch angle on creep damage have been investigated. The results show that the creep damage initiates in the filler metal. Different notch types bring different stress states, and generate different stress triaxialities and equivalent creep strains (CEEQs), leading to different creep damages. The maximum creep damage is generated in the notch tip for V-type notch, while the maximum creep damage is located at 0.4 mm away from the notch tip for C-type notch. For U-type notch, the location of the maximum creep damage moves from the notch tip to the inside gradually as the notch radius increases. With the increase of notch radius and notch angle, the failure time of creep damage increases for U-type and V-type notches, while it decreases for C-type notch. The creep failure is prone to happen to V-type notch because it belongs to sharp notch.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

Creep properties of a U‐type notch plate in Ni‐based superalloy

In the present investigation, the effect of notch on creep rupture behavior and creep rupture life of a Ni‐based superalloy has been assessed by performing creep tests on smooth and U‐notched plate specimen under 0°C. The finite element analysis coupled with continuum damage mechanics are carried out to understand the stress distribution across the notch throat and the creep damage evolution under multi‐axial stress state. The creep rupture life of U‐notched specimen is much larger than that of plane plate specimen under the same stress condition, indicating that there is a strengthening effect on notch specimen. Creep rupture life increases with increasing the notch radius, the smaller notch radius can induce the creep rupture easier. The effect of notch on the creep damage is also studied. It is found that the location of the maximum creep damage and the maximum equivalent creep strain initiates first at the notch root and gradually moves to the inside as the notch radius increases.     

Multi-axial fatigue behaviour of a severely notched carbon steel

The paper deals with multi-axial fatigue strength of notched specimens made of C40 carbon steel (normalised state), subjected to combined tension and torsion loading, both in-phase and out-of-phase (Φ=0 and 90°). V-notched specimens have been tested under two nominal load ratios, R=−1 and 0, while keeping constant and equal to the unity the biaxiality ratio, λ=σ_a/τ_a. All specimens have the same geometry, with notch tip radius and depth equal to 0.5 and 4 mm, respectively, while the V-notch angle is equal to 90°. The results determined are discussed together with those deduced under pure tension or torsion loading on plain and notched specimens as well as on small shafts with shoulders. The application of an energy-based approach allows all the fatigue data obtained from the notched specimens to be summarised in a single scatter band, in terms of the total strain energy density evaluated at the notch tip against cycles to failure.     

Translaminar fracture toughness: The critical notch tip radius of 0° plies in CFRP

The relationship between translaminar fracture toughness measured at initiation and specimen initial notch root radius is investigated for the translaminar failure mode of cross-ply IM7/8552 carbon/epoxy laminates. Compact tension specimens with four sizes of notch root radii were tested; the true initiation toughness of the laminate was measured from specimens with notch tip radii of ρ ? 250 μm. Testing of specimens with larger notch root radii, ρ = 750 μm, yielded an apparent toughness that was found to be 30% higher than the true toughness of the laminate. The propagation toughness corresponding to the R-curve plateau was found not to be affected by the initial notch tip radius. Investigation of the fracture surfaces of failed specimens revealed that there is no interaction between the 0° and 90° ply failure mechanisms, and that the critical notch radius is a property intrinsic to the 0° plies of the laminate.     

Fatigue strength of notched specimens made of 40CrMoV13.9 under multiaxial loading

The work deals with multiaxial fatigue strength of notched round bars made of 40CrMoV13.9 steel and tested under combined tension and torsion loading, both in-phase and out-of-phase. The axis-symmetric V-notches present a constant notch root radius, 1 mm, and a notch opening angle of 90°; the notch root radius is equal to 4 mm in the semi-circular notches where the strength in the high cycle fatigue regime is usually controlled by the theoretical stress concentration factor, being the notch root radius large enough to result in a notch sensitivity index equals to unity. In both geometries the diameter of the net transverse area is 12 mm.The results from multi-axial tests are discussed together with those obtained under pure tension and pure torsion loading from notched specimens with the same geometry. Altogether more than 120 new fatigue data are summarised in the present work, corresponding to a one-year of testing programme.All fatigue data are presented first in terms of nominal stress amplitudes referred to the net area and then re-analysed in terms of the mean value of the strain energy density evaluated over a given, crescent shape volume embracing the stress concentration region. For the specific steel, the radius of the control volume is found to be independent of the loading mode.     

纤维编织网增强混凝土侧面加固偏压短柱试验研究

纤维编织网增强混凝土具有耐腐蚀、耐高温、限裂效果好、施工便捷、几乎不增加结构尺寸等突出性能而逐渐成为近期研究的热点。开展TRC侧面加固偏压短柱试验, 探讨偏心距、前期受力历史和纤维编织网用量对加固效果的影响。试验结果表明:TRC侧面加固方法适合于大偏心受压结构, 偏心距越大, 增强效果越明显;结构前期受力历史对加固效果影响非常明显, 随着前期历史载荷的增大, 加固效果明显减弱;提高纤维编织网用量在一定程度上可以增强加固效果, 但增强幅度随用量的增加呈现出减弱趋势。在室内试验与相关研究成果的基础上, 提出了纤维编织增强混凝土侧面加固偏压短柱极限承载力计算方法, 计算值与试验值吻合较好。     

Plasticity spread in mild steel pre-cracked charpy bars

During dynamic service loading, small fatigue cracks are normally seen to emanate from the root of sharp machined stress concentration region. In a recent authors' paper at ICF4, the fracture strength of a charpy type notched beam has been studied in three different engineering materials, when a small fatigue crack emanates from the notch root. Fracture tests on these medium and high strength materials demonstrate the presence of a large size plastic zone near the crack tip [1–6]. To understand the mechanism of fracture for such complex geometry. it is important to know the size and shape of these plastically yielded regions. The present paper is mainly on the experimental measurement of plasticity spread as well as the stress intensity factor (S.I.F.) for such short cracks. Firstly, the S.I.F. is approximately measured by plain transmission photoelasticity on model castolite specimens. Secondly, plastic zones around crack tip are measured for a wide range of notch root radii and crack-length, by using photo-stress PS-3B coating on mild steel pre-cracked charpy type notched specimens. It is observed that for small scale yielding at the crack tip, the plasticity spread is around 60–65° angle to the line of crack-extension. On the contrary, as the gross applied stress approaches the yield strength of the material, the maximum plasticity spreads around 45° angle. Finally, it is noticed that at high stress level, the plastic zone boundary (for short crack) touches the free machined notch surface. These experimental observations explain the nature and degree of non-linearity in a load—C.O.D. diagram during the fracture test of a short cracked-notched specimen. These data are also useful to predict the crack-extension load for an elastic-plastic material.     

J-Integral for Deep and Shallow Notches Under Torsion

J-integral has been calculated along the free-of-stress border of deep and shallow rounded notches under torsion, under the hypothesis of a linear elastic behaviour of the material. Two exact closed-form solutions have been obtained which make it explicit the influence of the notch opening angle and the notch root radius. When the notch root radius tends to zero the proposed solution matches the expression for the corresponding pointed V-notch case.     

Gibt es eine Universalkerbkontur nach dem Vorbild der Natur?

Notch stresses are bending stresses due to the deformation of the notch contour line which are superimposed to the nominal stresses. This dual nature of the overall stresses allows to generate an uniform stress state along the notch contour by increasing the superimposed bending stress in the same way as the nominal stress decreases. This was possible till now by CAO (Computer Aided Optimization) [1,2] which simulates tree growth. However a FEM‐program and CAO‐software were necessary. By this deeper understanding of the nature of notch stresses a simple pocket calculator can do the job. Even a pair of compasses and a 45° angle can help. The optimized notch shapes are very similar, so it seems that a universal notch shape might exist under certain circumstances. Fatigue tests by swelling bending proof the success by drastic increase of the number of load cycles until failure.     

Dynamic fracture toughness testing of epoxy resin filled with sio2 particles

The fracture behavior of epoxy resin used as one of electrical insulation materials is generally brittle compared with that of metals. Therefore, when epoxy resin is used as a structural material, the effect of impact loading must be taken into consideration in design. In the present study, the dynamic fracture toughness of epoxy resin filled with SiO₂ particles has been evaluated both by the absorbed energy method and by the impact load obtained from the instrumented Charpy type impact test. Therefore, the absorbed energy has been analysed to evaluate the real fracture toughness. Moreover, the influence of inertial loading on the impact load must be also considered; therefore, the dynamic fracture toughness has been evaluated by the formula taking the inertial loading effect into consideration. Thus both fracture toughness values evaluated from absorbed energy and from impact load have been compared; as a result, a good agreement has been ascertained.It is common to perform impact test on specimens with blunt notches since they are easy to be prepared. However, variation of fracture toughness with notch root radius in the brittle material cannot be ignored. Therefore, the influence of notch root radius on the fracture toughness has been examined. As a result, it has been ascertained that the variation of fracture toughness with notch root radius follows the formula presented by Williams.     

Investigation on crystallographic behaviors of nickel‐base single crystal alloy cooling holes with different spanwise injection angles

Film cooling as an important thermal protection technology is widely used in aviation and ground gas turbine blades. But film cooling holes reduce the strength of blade seriously, which have become a key region of crack nucleation. In this paper, the plastic behaviors of nickel‐base single crystal alloy turbine cooling holes in spanwise injection angles range from 0° to 40° are investigated on basis of crystallographic constitutive theory. The results show that there are both higher stress regions and lower stress regions around multi‐column cooling holes, where suffer stress interference. The maximum Mises stress occurs at the hole in the center column. The places where the maximum resolved shear stresses occurs change with load and spanwise injection angle. The maximum Mises stress around holes with injection angle of 0° is lowest. With the injection angle increases, the maximum Mises stress increases until injection angles up to 30°. In all the slip systems, the resolved shear stress of hexahedral slip system is most sensitive to the changing of spanwise injection angle and load.     

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.     

Some Expressions for the Strain Energy in a Finite Volume Surrounding the Root of Blunt V-notches

The paper gives some closed form expressions for the strain energy averaged in a finite size volume surrounding the root of blunt V-shaped notches under Mode I loading. The control volume, reminiscent of Neuber’s concept of elementary structural volumes, is thought of as dependent on the ultimate tensile strength and the fracture toughness K_IC in the case of brittle or quasi-brittle materials subjected to static loads. Expressions for strain energy density under plane strain conditions and Mode I loading have been derived from an analytical frame recently reported in the literature, which matches Williams and Creager-Paris’ solutions in the particular cases of plates weakened by sharp V-notches or blunt cracks (U-notches), respectively. In order to validate a local-strain-energy based approach, a well-documented set of experimental data recently reported in this journal by Gómez and Elices has been used. Data refer to blunt and sharp V-specimens of PMMA subjected to static tension loads and characterised by a large variability of notch root radius (from 0 to 4.0 mm) and notch angle (from 0° to 150°). Critical loads obtained experimentally have been compared with the theoretical ones, estimated here by keeping constant the mean value of the strain energy in a well-defined small size volume.     

火灾后型钢混凝土柱抗震性能试验研究

该文进行了8个大比例型钢混凝土柱试件温度场和火灾后抗震性能试验,研究了升降温作用下柱试件的温度场分布规律以及火灾后受低周反复荷载时破坏规律。同时,考虑受火时间、轴压比、栓钉、含钢率等参数的影响,对火灾后型钢混凝土柱试件的典型破坏形态、滞回曲线的形状、加卸载刚度、承载能力等特性进行了系统的试验研究。研究表明:火灾升降温作用下,试件内部升温呈现出较大滞后性;火灾后柱试件出现了塑性铰区的破坏,受火时间越长,塑性铰长度越长;滞回环总体上呈梭形,耗能能力较好,滞回环有轻微的捏拢效应;随受火时间增加,试件承载能力降低;随轴压比增加,承载能力增加,延性降低;栓钉对试件承载能力影响不大。     

Orowan mechanism for abrupt localized flow and fracture initiation in metals ahead of an yielding notch

Plane strain elastic-plastic stresses are determined in Mises yielding solid at the root of an yielding crack like notch. This external edge notch is infinitely deep, and has a small finite (fixed) flank angle with a small tip root blunting radius. A boundary value type approach has been followed throughout, to solve this famous Orowan-lrwin problem. Firstly, a fictitious elastic stress field is calculated, considering a misfit in the bulk volume loading; these elastic stress expressions are valid when the notch is fully loaded. Secondly, the plastic stresses are determined in the compressibility gradient, maintaining the continuity of stresses and their derivatives at the yielded-unyielded interface. Our calculations reveal that: Orowan mechanism is fairly dominant below the notch root, as well as on ± 45° planes. It is concluded that the flow-localization in the Mises solid is due to a reverse slip, caused by the sudden release of a favourable critical mismatch stress concentration. Some elastic strain energy density is seen to be getting released from the bulk volume, while unloading the misfit load. The mismatch has been created entirely due to the compressibility-incompressibility difference, as suggested by Orowan.

Following Orowan, it is shown here that, before the onset of a stable crack extension, the increase in stress concentration at the notch tip root, is directly proportional to the strength of mismatch strain-localization below the notch, and inversely proportional to the plane strain plastic zone size on the crack extension plane. For a large scale yielding situation, compressive stresses and pure distortion regions are seen to occur at a far field within the plastic enclave.