Hygrothermal effects on multilayered composite plates using a refined higher order theory

A four-node quadrilateral plate element based on the global–local higher order theory (GLHOT) is proposed to study the response of laminated composite plates due to a variation in temperature and moisture concentrations. C⁰$C^0$ and C¹$C^1$ continuities are required in the transverse displacement functions as the first and the second derivatives are involved in the computation of the strain components in GLHOT [Int J Mech Sci, 2007; 49:1276–1288]. In this paper, a displacement function satisfying C⁰$C^0$ continuity is constructed by using the refined element method, and the discrete Kirchhoff quadrilateral thin plate element DKQ is employed for satisfying the requirement of C¹$C^1$ continuity. The effects of temperature and moisture concentrations on the material properties and the hygrothermal response of multilayered plates are studied, in contrast to most of the previous investigations in which the material properties are assumed to be independent of temperature. Hygrothermal response due to a variation in temperature and moisture concentrations has been studied for different material types sensitive to changing hygrothermal environment conditions. Numerical results suggest that temperature-dependent material properties ought to be used in the analysis of laminated plates subjected to hygrothermal loads.     

Interlaminar stress recovery for three-dimensional finite elements

An accurate evaluation of interlaminar stresses in multilayer composite laminates is crucial for the correct prediction of the onset of delamination. In general, three-dimensional finite element models are required for acceptable accuracy, especially near free edges and stress concentrations. Interlaminar stresses are continuous both across and along layer interfaces. Nonetheless, the continuity of interlaminar stresses is difficult to enforce in C⁰$C^0$ interpolated elements. Nodal values of the stresses are usually retrieved using extrapolation techniques from super-convergent points, if known, or Gauss points inside the element. Stress fields within an element can be deduced using either constitutive relations or variationally consistent procedures. In either case, spurious oscillations in stress fields may be encountered leading to a reduced accuracy of the recovered stresses at nodes. In this paper, an efficient interlaminar stress recovery procedure for three-dimensional finite element formulations is presented. The proposed procedure does not rely on extrapolation techniques from super-convergent or integration points. Interlaminar stress values are retrieved directly at nodes and stress continuity at the inter-element boundary is automatically satisfied. Several benchmark problems were analysed. Comparisons with finite element software and available solutions in the literature confirmed the accuracy of the procedure. Accurate interlaminar stresses were obtained using coarser meshes compared to customary recovery procedures.     

Interlaminar shear stresses around an internal part-through hole in a laminated composite plate

The equilibrium/compatibility method, which is a semi-analytical post-processing method, is employed for computation of hitherto unavailable through-thickness variation of interlaminar (transverse) shear stresses in the vicinity of the bi-layer interface circumferential re-entrant corner line of an internal part-through circular cylindrical hole weakening an edge-loaded laminated composite plate. A C^o${\text{C}}^{\text{o}}$-type triangular composite plate element, based on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST), is utilized to first compute the in-plane stresses and layer-wise through-thickness average interlaminar shear stresses, which serve as the starting point for computation of through-thickness distribution of interlaminar shear stresses in the vicinity of the bi-layer interface circumferential re-entrant corner line of the part-through hole. The same stresses computed by the conventional equilibrium method (EM) are, in contrast, in serious error in the presence of the bi-layer interface circumferential re-entrant corner line singularity arising out of the internal part-through hole, and are found to violate the interfacial compatibility condition. The computed interlaminar shear stress can vary from negative to positive through the thickness of a cross-ply plate in the neighborhood of this kind of stress singularity.     

A C-type higher-order theory for bending analysis of laminated composite and sandwich plates

In this paper, a C⁰-type higher-order theory is developed for bending analysis of laminated composite and sandwich plates subjected to thermal/mechanical loads. The total number of unknowns in the present theory is independent of number of layers. The continuity conditions of transverse shear stresses at interfaces are a priori enforced. Moreover, the conditions of zero transverse shear stresses on the upper and lower surfaces are also considered. Based on the developed higher order theory, the typical solutions are presented for comparison. It is very important that the first derivatives of transverse displacement w have been taken out from the in-plane displacement fields of the proposed model, so that its finite element counterparts may avoid using the C¹ interpolation functions. To assess the developed theory, the C¹-type higher-order theory is chosen for comparison. Numerical results show that the present model can accurately predict the thermal/mechanical response of laminated composite and sandwich plates. Moreover, the present model is able to accurately calculated transverse shear stresses directly from constitutive equations without any postprocessing methods.     

The Analysis of the Gelling Time of Gelatin by a Thermal Sensor Method

Abstract

It has been known that the setting time of gelatin solution may be measured readily by the thermal sensor method. The relation between the setting time (t), the solution concentration (C) and the cooling temperature (T) could be represented empirically as In$$t=a?{(C/T)}^{?1}+b.$$ (a,b: the coefficients). In the present paper, the relation of these three factors is re-examined and the following empirical formula proposed.

$$t=a?{(C/T)}^{?1}+b.$$

This equation is applied to two types of the 4th IAG gelatins (M-8929, PB-1185) to find their gelling characteristics and the correlation between the t-value and the C/T value. This empirical formula could consequently be employed in the study of these relationships for gelatin solution concentrations in the range 4 % to 10 %.     

Dynamic fracture of carbon nanotube/epoxy composites under high strain-rate loading

We investigate dynamic fracture of three types of multiwalled carbon nanotube (MWCNT)/epoxy composites and neat epoxy under high strain-rate loading (${10}^5''–''{10}^6$ s⁻¹). The composites include randomly dispersed, 1 wt%, functionalized and pristine CNT/epoxy composites, as well as laminated, ∼50 wt% CNT buckypaper/epoxy composites. The pristine and functionalized CNT composites demonstrate spall strength and fracture toughness slightly higher and lower than that of neat epoxy, respectively, and the spall strength of laminated CNT buckypaper/epoxy composites is considerably lower; both types of CNTs reduce the extent of damage. Pullout, sliding and immediate fracture modes are observed; the fracture mechanisms depend on the CNT–epoxy interface strength and fiber strength, and other microstructures such as the interface between CNT laminates. Compared to the functionalized CNT composites, weaker CNT–epoxy interface strength and higher fiber strength lead to a higher probability of sliding fracture and higher tensile strength in the pristine CNT composites at high strain rates. On the contrary, sliding fracture is more pronounced in the functionalized CNT composites under quasistatic loading, a manifestation of a loading-rate effect on fracture modes. Despite their helpful sliding fracture mode and large CNT content, the weak laminate–laminate interfaces play a detrimental role in fracture of the laminated CNT buckypaper/epoxy composites. Regardless of materials, increasing strain rates leads to pronounced rise in tensile strength and fracture toughness.