An analytical assessment of the influence of skin imperfections on the indentation collapse mechanism in composite sandwich beams

The influence of skin imperfections, in the form of delamination damage or thickness variations, on the indentation collapse mechanism in composite sandwich beams with compressive yielding cores is studied using the models of non-prismatic beam and beam-column resting on a nonlinear Winkler foundation. Upper and lower threshold solutions are derived for the indentation response and collapse load and the transition between the two limits is defined as a function of size, magnitude and position of the imperfections. In beams where global bending effects are not negligible, the collapse load is limited from above by the indentation collapse load of beams with rigid-plastic cores and the face wrinkling collapse load of beams with elastic cores; the transition between the two limits is controlled by material/structure properties and the magnitude of the imperfections. Characteristic lengths, which depend on material and geometrical properties, define the minimum size of the imperfections with the strongest effect on the solution and the minimum distance between load and imperfections with no effect on the solution.     

Static indentation and unloading response of sandwich beams

This paper deals with analysis of foam core sandwich beams subject to static indentation and subsequent unloading (removal of load). Sandwich beams are assumed continuously supported by a rigid platen to eliminate global bending. An analytical model is presented assuming an elastic-perfectly plastic compressive behaviour of the foam core. An elastic part of indentation response is described using the Winkler foundation model. Upon removal of the load, an elastic unloading response of the foam core is assumed. Also, finite element (FE) analysis of static indentation and unloading of sandwich beams is performed using the FE code ABAQUS. The foam core is modelled using the crushable foam material model. To obtain input data for the analytical model and to calibrate the crushable foam model in FE analysis, the response of the foam core is experimentally characterized in uniaxial compression, up to densification, with subsequent unloading and tension until tensile fracture. Both models can predict load–displacement response of sandwich beams under static indentation and a residual dent magnitude in the face sheet after unloading along with residual strain levels in the foam core at the unloaded equilibrium state. The analytical and FE analyses are experimentally verified through static indentation tests of composite sandwich beams with two different foam cores. The load–displacement response, size of a crushed core zone and the depth of a residual dent are measured in the testing. A digital speckle photography technique is also used in the indentation tests in order to measure the strain levels in the crushed core zone. The experimental results are in good agreement with the analytical and FE analyses.     

Collapse of clamped and simply supported composite sandwich beams in three-point bending

Composite sandwich beams, comprising glass–vinylester face sheets and a PVC foam core, have been manufactured and tested quasi-statically. Clamped and simply supported beams were tested in three-point bending in order to investigate the initial collapse modes, the mechanisms that govern the post-yield deformation and parameters that set the ultimate strength of these beams. Initial collapse is by three competing mechanisms: face microbuckling, core shear and indentation. Simple formulae for the initial collapse loads of clamped and simply supported beams along with analytical expressions for the finite deflection behaviour of clamped beams are presented. The simply supported beams display a softening post-yield response, while the clamped beams exhibit hardening behaviour due to membrane stretching of the face sheets. Good agreement is found between the measured, analytical and finite element predictions of the load versus deflection response of the simply supported and clamped beams. Collapse mechanism maps with contours of initial collapse load and energy absorption are plotted. These maps are used to determine the minimum mass designs of sandwich beams comprising woven glass face sheets and a PVC foam core.     

Indentation study of Z-pin reinforced polymer foam core sandwich structures

Z-pin reinforced foam core sandwich panels with composite face sheets, supported on a rigid base and subjected to quasi-static indentation using spherical indenter was studied in this paper. The effects of configurations of Z-pin, including inclination angle and pinning density, on the load–indentation response were studied, and the resulting damage modes were investigated. The effect of inclination angle of pin on the load–indentation behavior is not notable compared with those of Z-pinning density and Z-pin configuration. The collapse of Z-pinned foam core is due to the buckling of pin, and the pin buckling is significantly dependent on the location of indenter. An approximate solution was developed based on the principle of minimum potential energy to simulate the indentation damage response of Z-pin reinforced foam core sandwich. The analytical predictions compare well with the experimental results.     

Parametric study of the post-buckling strength of structural core sandwich panels

Post-buckling strength of simply supported orthotropic corrugated board panels subjected to edge compressive loading has been investigated using geometrically non-linear finite element analysis (FEA). Adjustments of the transverse shear stiffnesses in the FEA were necessary and performed by comparing the critical buckling load calculated by FEA with a closed form solution. The collapse load of the sandwich plate was calculated based on material failure of the facings predicted from Tsai-Wu failure theory. Parametric studies were performed to investigate the sensitivity of the collapse load to changes in the transverse shear stiffnesses of the core, initial out-of-plane imperfections, asymmetry in board construction, slenderness ratio and eccentric loading of the plate. It was found that a reduction of the transverse shear stiffnesses of the core below a certain limit produces a significant reduction in the collapse load. Panels are said to be insensitive to imperfections and this holds true when the imperfections are the same as or lesser than the thickness of the panel, but a 40% reduction of the collapse load is observed for imperfections that are ten times the panel thickness. From a design point of view it is shown that a symmetrical board is preferred because an asymmetric board as well as eccentric loading of the panel significantly reduce the collapse load. It is also shown that the critical buckling load is directly related to the slenderness ratio of the panel whereas the collapse load is not.     

The flatwise compressive properties of Nomex honeycomb core with debonding imperfections in the double cell wall

Mechanical properties of Nomex honeycomb core are governed by not only its global dimensions, cell topology, material properties and proportion of the aramid paper and phenolic resin, but also possible manufacturing imperfections, such as the debonding between the two aramid paper sheets in the double cell wall. To account for the layered feature of the cell walls and the bonding conditions between aramid paper sheets, a three-dimensional unit cell model was proposed and developed in this study. The aramid paper sheets, the phenolic resin coating, the adhesive between the aramid paper sheets, and their bonding relationships were all explicitly modelled in accordance with their actual geometry and material parameters. The model was validated by comparing the predicted load-displacement curves and failure modes with the test results. The effects of representative bonding imperfections on both the collapse load and the related displacement of the honeycomb core under flatwise compression were evaluated. Through the analyses, it was found that the debonding imperfections have significant effects on the mechanical behaviour of the honeycomb core and that with the same debonding area the debonding at the outside edge of the adhesive printing line is the most critical. It was also found that debonding fracture may occur if adhesive is not strong enough or the debonding imperfection area is large.     

A contact size-independent approach to the estimation of biaxial residual stresses by Knoop indentation

The presence of residual stresses (RS) in a material causes a shift of the indentation load–displacement curve. The resulting change in the Kick's law coefficient C can hence be exploited to estimate these RS. By contrast with axisymmetric indenters, when employing the Knoop indenter with its large aspect-ratio, C is further sensitive to the indenter's orientation with respect to the principal RS directions. For a wide range of material properties, maximum and minimum C values are obtained by finite element analysis. It is observed that the RS ratio can be estimated directly from the C ratio, independent of magnitude and sign of RS. Further, the finding that C values for the non-equibiaxial RS case can be converted to equivalent C values for two equibiaxial RS cases, made for conical indentation (J.H. Lee et al., 2010, J Mater Res 25: 2212–2223), is shown to apply to Knoop indentation, too. The magnitude of RS can thus be determined from the equibiaxial RS case. The equibiaxial RS case is investigated in detail and mapping functions are established between C and the corresponding RS value. Finally the method is validated experimentally by comparison with Knoop indentation of bended cross-shaped steel specimens.     

Anticlastic effects and the transition from narrow to wide behavior in orthotropic beams

The classical assumptions of standard beam theory include that of uniaxial stress for isotropic beams, or vanishing transverse moment for beams of layered orthotropic materials. Wide beams, on the other hand, display the familiar effect in which the transverse “anticlastic” curvature is assumed to vanish. The transition between these behaviors is not well characterized, and is addressed in the present work by means of a solution for orthotropic plates with two free lateral edges, so as to represent a beam of any aspect ratio. It is found that the transition is independent of the thickness, but depends on the length/width aspect ratio and the material properties. The calculations show that the deviation from narrow beam behavior occurs at a length/width aspect ratio of about 10 for isotropic and many orthotropic materials, and depends on the orthotropic material properties. Comparisons with experimental data in the literature support these conclusions.     

高比强高孔隙率泡沫铝合金三明治梁

研究了高比强泡沫铝合金和泡沫纯铝的单向压缩和剪切性能,对以高比强泡沫铝合金为夹芯的三明治梁失效模式的尺寸范围和承载能力进行了理论计算,结果与实验结果符合得很好.给出了泡沫铝合金三明治梁的设计方法,表明在较小的设计载荷下,三明治梁是以刚度作为设计的控制条件;在较大的设计载荷下,以相对强度为设计的控制条件.泡沫铝合金三明治梁与泡沫纯铝三明治梁的对比表明,在刚度设计控制条件下,前者的刚度是后者的1.00～1.185倍.在强度设计控制条件下,剪切破坏和压凹破坏失效模式下的泡沫铝合金三明治梁比泡沫纯铝三明治梁的极限强度分别提高57%～180%和90%～220%.     

A simple framework of spherical indentation for measuring elastoplastic properties

Based on the indentation load–displacement curve, spherical indentation may deduce material elastoplastic properties from the measurements at several depths (which mimics the dual/plural sharp indentation method). The previous approaches, however, have very complex formulations and involve many fitting parameters that lack theoretical backgrounds; moreover, studies based on shallow indentation may not lead to unique solution. To close these gaps, we propose a simple framework of spherical indentation based on a new limit analysis-based representative strain analysis, which contains minimum number of fitting parameters. Two simple equations of the normalized loading work (at two different depths) are proposed, which can determine the material plastic properties accurately from the loading curve. In addition, by using either the established Fischer-Cripps method or an extra equation based on the contact stiffness, both the elastic and plastic properties are determined with reasonable accuracy. The simple framework may be useful for guiding the measurement of elastoplastic properties via spherical indentation.     

陶瓷材料压痕韧性的统计性质

采用直接压痕法测定了钠钙硅酸盐玻璃和一种ＴｉＣ 颗粒增强Ａｌ_２Ｏ_３复合材料的断裂韧性．研究表明,在同一压痕压制荷载下测得的同一种材料的压痕韧性呈现出较大离散性,可以采用Ｗｅｉｂｕｌｌ分布加以较好地描述．对两种材料的试验数据的对比分析指出,压痕韧性测试值的离散性反映了材料显微结构的不均匀性对材料局部裂纹扩展阻力的影响．基于这一分析,本文建议采用直接压痕法测定材料断裂韧性时,应尽可能增大试验量,从而对压痕韧性测试结果的统计性质作出完整描述．     

Study of indentation size effect and microhardness of SrLaAlO<Subscript>4</Subscript> and SrLaGaO<Subscript>4</Subscript> single crystals

The load dependence of the Vickers microhardness of SrLaAlO₄ and SrLaGaO₄ single crystals, using a PMT-3 hardness tester, has been investigated and analysed from the standpoint of various theoretical models. On the (100) and (001) planes of these crystals, reverse indentation size effect was observed. Analysis of the experimental data revealed: (1) the indentation size effect is best described by Meyer's law and the proportional specimen resistance model of Li and Bradt, (2) indentation-induced cracking model for reverse indentation size effect and Meyer's law cannot be used to determine the hardness of the crystals, (3) as shown by the negative values of the load-dependent quantities in Hays-Kendall's approach and Li-Bradt model, the origin of indentation size effect is associated with the processes of relaxation of indentation stresses, and (4) the load-dependent and load-independent quantities of different models are interrelated and are intimately connected with the orientation and chemical composition of the crystals. It was also found that the plots of the ratio of indentation load to indentation diagonal against indentation diagonal for a sample exhibit two different slopes with a transition in the slopes occurring at an indentation diagonal, whose value depends on the indenter orientation, indented plane and chemical composition of the crystals. The physical significance of the appearance of these transitions and the nature of load-independent indentation microhardness are discussed. Electronic Publication     

New developments for fracture toughness determination by Vickers indentation

Abstract

Indentation is a traditional method used to determine the toughness of brittle materials. Different models are used for the calculation depending on the shape of the cracks that are initiated and developed as a result of the indentation. Recently it was observed that a transition between Palmqvist and median cracks is possible when increasing the indentation load. In the present study it is shown that this transition is not as sharp as is generally supposed, but is rather smooth. In these conditions standard calculation procedures cannot be applied. A new methodology is proposed here, which allows the calculation of a unique toughness value on the basis of the determination of the limits of the material cracking tendency.     

泡沫铝层合梁的三点弯曲变形

研究了泡沫铝层合梁三点弯曲的载荷(P)-位移(δ)曲线、变形过程及面板破坏、夹芯剪切破坏、凹陷破坏等破坏模式。用极限载荷公式得到的计算值与实验值符合良好。实验所得的加载和卸载刚度(P/δ)与计算结果吻合较好。泡沫铝层合梁具有较低的密度((0.42～0.92)×10~3kg/m~3)和很高的弯曲比刚度(E~(1/2)/ρ)。利用极限载荷公式建立了破坏模式图。     

Experimental study of fracture of lightly reinforced concrete beams

The experimental program reported in this paper was planned to investigate the sensitivity of lightly reinforced concrete beams to size and to steel-to-concrete bond properties. Forty-eight micro-concrete reinforced beams were tested; these were of three different sizes, reinforced with various amounts of both smooth and ribbed wires. Unlike the tests found in the scientific literature, the material properties and the parameters that characterize the steel-concrete interaction were all obtained from independent tests. Likewise, experimental errors due to material heterogeneity or incorrect setup of the tests were minimized so as to ensure a high level of control during the execution of the program. The experimental results exhibit maximum load size effect and a strong dependence on bond-slip properties. Beams with a large cover show a secondary load peak between cover cracking and steel yielding, which provides a hint as to the role of the reinforcement cover in the cracking process.     

“Segment-wise model” for theoretical simulation of barely visible indentation damage in composite sandwich beams: Part II – Experimental verification and discussion

When localized transverse loading is applied to a sandwich structure, the facesheet locally deflects and the core crushes. A residual dent induced by the core crushing significantly degrades the mechanical properties of the sandwich structure. In a previous paper, the authors established a “segment-wise model” for theoretical simulation of barely visible indentation damage in honeycomb sandwich beams with composite facesheets. Honeycomb sandwich beam was divided into many segments based on the periodic shape of the honeycomb and complicated through-thickness characteristics of the core were integrated into each segment. In this paper, the new model is validated by experiments using specimens with different types of honeycomb cores. In addition, the damage growth mechanism under indentation load was clarified from the viewpoint of the reaction force from the core to the facesheet. The applicability of the model to other types of core materials is also discussed.     

An energy-balance analysis for the size effect in low-load hardness testing

The size effect in low-load hardness testing is analyzed theoretically using an energy-balance approach. A new semi-empirical equation is proposed to correlate the hardness test load and the resulting indentation size. The validity of this new equation is verified by analyzing the previously reported experimental data. It is found that the value of true hardness of material estimated with this new equation is independent of the indentor geometry as well as indentation size.     

Characterization of the material from the induction healing porous asphalt concrete trial section

An induction healing approach was developed to increase the service life of porous asphalt wearing course. Steel wool fibers were mixed in the asphalt mixtures, and then induction heating was applied to heat up the localized steel wool fibers in asphalt mixtures when damage is expected. As a result of induction heating, possible cracks and damages inside porous asphalt can be healed. The objective of this paper is to characterize the field obtained material from an induction healing porous asphalt trial section with laboratory experiments. Heating speed of the field cores was first measured with an infrared camera. It was found that these cores with steel wool can be heated with induction energy. Then, the particle loss value, indirect tensile strength, water sensitivity and nano indentation modulus of the field cores were studied. The results indicate that the addition of steel wool improves the particle loss resistance and ductility of the porous asphalt concrete cores. The mortar phase in porous asphalt core with steel wool shows higher indentation modulus than that in the plain core. These findings imply that steel wool can increase the ravelling resistance of porous asphalt concrete. Finally, the fatigue life extension parameter in four point bending test was applied to investigate the healing potential of this porous asphalt mixture with and without induction heating. The fatigue life of the beams can be greatly extended with induction heating. It was also found that the aged beams can heal much more and faster with induction heating than that with natural healing. Based on these findings, it is expected that the durability of porous asphalt pavement will be improved by the reinforcement of steel wool and induction healing.     

Characterizing the surface contact behaviour of ceramics

The indentation hardness of four glass-bonded ceramics has been examined as a function of load and temperature, It has been observed that the relative hardness values may interchange depending on the temperature and load of testing. For each material there are two regimes of temperature dependence. A has been possible to qualitatively correlate the transition temperature with the composition of the glassy binder phase.     

Evaluation of the elastic modulus of thin film considering the substrate effect and geometry effect of indenter tip

A method using finite element method (FEM) is proposed to evaluate the geometry effect of indenter tip on indentation behavior of film/substrate system. For the nanoindentation of film/substrate system, the power function relationship is proposed to describe the loading curve of the thin film indentation process due to substrate effect. The exponent of the power function and the maximum indentation load can reflect the geometry effect of indenter and substrate effect. In the forward analysis, FEM is used to simulate the indentation behavior of thin film with different apex angles of numerical conical indenter tip, and maximum indentation load and loading curve exponent are obtained from the numerical loading curves. Meanwhile, the dimensionless equations between the loading curve exponent, the maximum load, elastic properties of film/substrate system and apex angle of indenter are established considering substrate effect. In the reverse analysis, a nanoindentation test was performed on thin film to obtain the maximum indentation load and the loading curve exponent, and then the experimental data is substituted into the dimensionless equations. The elastic modulus of thin film and the real apex angle of indenter can be obtained by solving the dimensionless equations. The results can be helpful to the measurement of the mechanical properties of thin films by means of nanoindentation.