Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions

The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.     

Toughening of a brittle thermosetting polymer: Effects of reinforcement particle size and volume fraction

Micron- and nanometer-sized aluminum particles were used as reinforcements to enhance the fracture toughness of a highly-crosslinked, nominally brittle, thermosetting unsaturated polyester resin. Both particle size and particle volume fraction were systematically varied to investigate their effects on the fracture behavior and the fracture toughness. It was observed that, in general, the overall fracture toughness increased monotonically with the volume fraction of aluminum particles, for a given particle size, provided particle dispersion and deagglomeration was maintained. The fracture toughness of the composite was also strongly influenced by the size of the reinforcement particles. Smaller particles led to a greater increase in fracture toughness for a given particle volume fraction. Scanning electron microscopy of the fracture surfaces was employed to establish crack front trapping as the primary extrinsic toughening mechanism. Finally, the effects of particle volume fraction and size on the tensile properties of the polyester-aluminum composite were also investigated. The measured elastic modulus was in accordance with the rule-of-mixtures. Meanwhile, the tensile strength was slightly reduced upon the inclusion of aluminum particles in the polyester matrix.     

Tuning the mechanical properties of glass fiber-reinforced bismaleimide–triazine resin composites by constructing a flexible bridge at the interface

Abstract

We demonstrate a new method that can simultaneously improve the strength and toughness of the glass fiber-reinforced bismaleimide–triazine (BT) resin composites by using polyethylene glycol (PEG) to construct a flexible bridge at the interface. The mechanical properties, including the elongation, ultimate tensile stress, Young’s modulus, toughness and dynamical mechanical properties were studied as a function of the length of PEG molecular chain. It was found that the PEG molecule acts as a bridge to link BT resin and glass fiber through covalent and non-covalent bondings, respectively, resulting in improved interfacial bonding. The incorporation of PEG produces an increase in elongation, ultimate tensile stress and toughness. The Young’s modulus and T_g were slightly reduced when the length of the PEG molecular chain was high. The elongation of the PEG-modified glass fiber-reinforced composites containing 5 wt% PEG-8000 increased by 67.1%, the ultimate tensile stress by 17.9% and the toughness by 78.2% compared to the unmodified one. This approach provides an efficient way to develop substrate material with improved strength and toughness for integrated circuit packaging applications.     

Crack growth resistance (R-curve) behaviour and thermo-physical properties of Al2O3 particle-reinforced AlN/Al matrix composites

Crack growth resistance behaviour and thermo-physical properties of Al₂O₃ particle-reinforced AlN/Al matrix composites have been studied as a function of AlN volume fraction as well as Al₂O₃ particle size. The fracture toughness of the composites decreased with increase in vol% AlN and decrease in Al₂O₃ particle size. All the composites exhibited R-curve behaviour which has been attributed to crack bridging by the intact metal ligaments behind the crack tip. The Young’s modulus of the composites increased with the vol% of AlN whereas the thermal diffusivity and coefficient of thermal expansion followed a reverse trend. The composites exhibited hysteresis in thermal expansion as a function of temperature and the hysteresis decreased with decrease in metal content of the composite.     

Failure mechanics in ternary composites of polypropylene with inorganic fillers and elastomer inclusions

The effects of phase morphology, interfacial adhesion and filler particle shape and volume fraction on the fracture toughness of polypropylene (PP) filled with CaCO₃ or Mg(OH)₂ and ethylene-propylene elastomer (EPR) were investigated. Separation of the inorganic filler and elastomer particles was achieved using maleic-anhydride-grafted PP (MPP) to enhance the inorganic filler-matrix adhesion. Encapsulation of the rigid filler by the elastomer was achieved by using maleic-anhydride-grafted EPR (MEPR) to increase the inorganic filler-elastomer adhesion. The two limiting morphologies differed significantly in fracture toughness under impact loading at the same material composition. A model for a mixed mode of failure, accounting for the plane strain and plane stress contributions to the strain energy release rate,G _c, was used to predict the upper and lower limits forG _c for the two limiting morphologies over an interval of elastomer volume fractions,v _e, from 0–0.2 at a constant filler volume fraction,V _f = 0.3, and over the filler volume fraction from 0–0.4 at constant EPR content. The role of material yield strength in controlling fracture toughness has been described successfully using Irwin's analysis of plastic zone size. The presence of elastomer enhances both the critical strain energy release rate for crack initiation,G _c, and the resistance to crack propagation as expressed by Charpy notched impact strength for the two limiting morphologies. Satisfactory agreement was found between the experimental data and predictions of upper and lowerG _c limits.     

Influence of thermal conditions on the tensile properties of basalt fiber reinforced polypropylene–clay nanocomposites

In this paper, a comparative study on the tensile properties of clay reinforced polypropylene (PP) nanocomposites (PPCN) and chopped basalt fiber reinforced PP–clay nanocomposites (PPCN-B) is presented. PP matrix are filled with 1, 3 and 5 wt.% of nanoclays. The ultimate tensile strength, yield strength, Young’s modulus and toughness are measured at various temperature conditions. The thermal conditions are included the room temperature (RT), low temperature (LT) and high temperature (HT). The basal spacing of clay in the composites is measured by X-ray diffraction (XRD). Nanoscale morphology of the samples is observed by transmission electron microscopy (TEM). Addition of nanoclay improves the yield strength and Young’s modulus of PPCN and PPCN-B; however, it reduces the ultimate tensile strength. Furthermore, the addition of chopped basalt fibers to PPCN improves the Young’s modulus of the composites. The Young’s modulus and the yield strength of both PPCN and PPCN-B are significantly high at LT (−196 °C), descend at RT (25 °C) and then low at HT (120 °C).     

Development of sizing-free multi-functional carbon fibre nanocomposites

High quality multi-walled carbon nanotubes (CNTs) grown at high density using a low temperature growth method are used as an alternative material to polymer sizing and is utilised in a series of epoxy composites reinforced with carbon fibres to provide improved physical and electrical properties. We report improvements for sizing-sensitive mechanical and physical properties, such as the interfacial adhesion, shear properties and handling of the fibres, whilst retaining resin-infusion capability. Following fibre volume fraction normalisation, the carbon nanotube-modified carbon fibre composite offers improvements of 146% increase in Young’s modulus; 20% increase in ultimate shear stress; 74% increase in shear chord modulus and an 83% improvement in the initial fracture toughness. The addition of CNTs imparts electrical functionalisation to the composite, enhancements in the surface direction are 400%, demonstrating a suitable route to sizing-free composites with enhanced mechanical and electrical functionality.     

Effective in situ material properties of micron-sized SiO2 particles in SiO2 particulate polymer composites

Several analytical models exist for determination of the Young’s modulus and coefficient of thermal expansion (CTE) of particulate composites. However, it is necessary to provide accurate material properties of the particles as input data to such analytical models in order to precisely predict the composite’s properties, particularly at high particle loading fractions. In fact, the constituent’s size scale often presents a technical challenge to accurately measure the particles’ properties such as Young’s modulus or CTE. Moreover, the in situ material properties of particles may not be the same as the corresponding bulk properties when the particles are embedded in a polymer matrix. To have a better understanding of the material properties and provide useful insight and design guidelines for particulate composites, the concept of “effective in situ constituent properties” and an indirect method were employed in this study. This approach allows for the indirect determination of the particle’s in situ material properties by combining the experimentally determined composite and matrix properties and finite element (FE) models for predicting the corresponding composite properties, then backing out the effective in situ particle properties. The proposed approach was demonstrated with micron-size SiO₂ particle reinforced epoxy composites over a range of particle loading fractions up to 35 vol.% by indirectly determining both the effective Young’s modulus and the effective CTE of the particles. To the best of our knowledge, this study is the first published report on the indirect determination of both the Young’s modulus and the CTE of micron size particles in particulate composites. Similar results on Young’s modulus of micron-size SiO₂ particles measured from nano-indentation testing are encouraging.     

聚氯乙烯/氧化石墨烯薄膜的力学性能和热稳定性能

通过溶液共混法制备了氧化石墨烯(GO)分散均匀的聚氯乙烯(PVC)/GO纳米复合薄膜,研究了薄膜的力学性能和热稳定性能。结果表明,微量GO能大幅度提高PVC的模量和拉伸强度,且保持较高的断裂伸长率。在PVC中添加质量分数为0.12%的GO,PVC的拉伸强度提高63%,杨氏模量提高20%;添加量为0.60%时,PVC的拉伸强度提高125%,杨氏模量提高126%.添加GO还能提高PVC的起始分解温度、最大分解温度以及PVC的成碳量。GO片层具有较高的强度和模量、GO在高分子基体内的均匀分散、GO和PVC之间较强的相互作用、GO与PVC的层状结构,是其力学性能提高的主要原因.     

纳米TiO2颗粒弱界面增强树脂基复合材料宏观力学行为有限元模拟

基于蒙特卡罗法, 编写了随机分布颗粒增强复合材料的二维代表体积单元生成程序, 建立了纳米颗粒增强树脂基复合材料的有限元模型, 其中采用双线性内聚力模型描述复合材料弱界面的应力与位移关系。通过纳米TiO₂ 颗粒增强环氧树脂基复合材料应力应变行为模拟结果与文献结果对比, 证明了模型的有效性。讨论了弱界面情况下, TiO₂颗粒质量分数与颗粒尺寸对复合材料宏观有效模量的影响, 并对复合材料弱界面渐进损伤过程进行了非线性分析。结果表明: 随着纳米TiO₂颗粒质量分数增加, 复合材料杨氏模量和断裂延伸率均有所增强, 但材料屈服强度有所降低; 相同颗粒质量分数情况下, 随着颗粒尺寸的增大, 颗粒与基体材料之间界面单元总长度减小, 复合材料断裂延伸率有所下降。     

黄麻纤维束力学性能的尺寸和应变率效应

为了探究黄麻纤维束的尺寸效应和应变率敏感性,利用C43电子式万能试验机和CEAST 9340落锤试验冲击系统分别在静动载条件下对黄麻纤维束进行测试,获得了杨氏模量、强度、峰值应变和韧性随标距和应变率的变化关系静载试验在1/600s-1应变率条件下进行,测试了6组不同标距(25、50、100、150、200和300mm)的试件;动载试验以应变率为变量,在4组不同的应变率(40、80、120和160s-1)条件下进行了测试,试件标距均为25mm。测试结果表明:随着试件标距增大,杨氏模量初始增大,当标距大于100mm时趋于稳定;强度、峰值应变和韧性均减小。随着应变率增大,杨氏模量和强度均增大;峰值应变初始减小后趋于稳定;韧性先减小后增大。鉴于植物纤维束材料较大的性能离散性,采用Weibull分布对试验数据进行拟合,获得了黄麻纤维束强度在不同试验条件(标距和应变率)下的分布规律。     

The effect of volume fraction of primary α phase on fracture toughness behaviour of Timetal 834 titanium alloy under mode I and mixed mode I/III loading

The effect of volume fraction of primary α phase on mode I and mixed mode I/III fracture toughness of Timetal 834 titanium alloy was investigated. The mode I and mixed mode I/III fracture toughness values for loading angle of 30° were found to initially decrease and subsequently increase with increase in volume fraction of primary α phase. On the other hand, mixed mode I/III fracture toughness for loading angle of 45° was found to monotonically decrease with increasing volume fraction of α phase. The fracture toughness was also found to marginally increase with increasing loading angle for the two lower primary α volume fractions, i.e. 6% and 15% whereas it marginally decreases with increasing loading angle for primary α volume fraction of 30%. The results were explained on the basis of the nature of stress field ahead of the crack tip under mixed mode I/III loading as well as the fracture mechanisms operative in this alloy for different α volume fractions.     

Room temperature elastic moduli and Vickers hardness of hot-pressed LLZO cubic garnet

Cubic garnet Li_6.24La₃Zr₂Al_0.24O_11.98 (LLZO) is a candidate material for use as an electrolyte in Li–Air and Li–S batteries. The use of LLZO in practical devices will require LLZO to have good mechanical integrity in terms of scratch resistance (hardness) and an adequate stiffness (elastic modulus). In this paper, the powders were fabricated by powder processing of cast ingots. All specimens were then densified via hot pressing. The room temperature elastic moduli (Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio) and hardness were measured by resonant ultrasound spectroscopy, and Vickers indentation, respectively. For volume fraction porosity, P, the Young’s modulus was 149.8?±?0.4?GPa (P?=?0.03) and 132.6?±?0.2?GPa (P?=?0.06). The mean Vickers hardness was 6.3?±?0.3?GPa for P?=?0.03 and 5.2?±?0.4 for P?=?0.06.     

Effect of processing parameters and clay volume fraction on the mechanical properties of epoxy-clay nanocomposites

The influence of processing parameters and particle volume fraction was experimentally studied for epoxy clay nanocomposites. Nanocomposites were prepared using onium ion surface modified montmorillonite (MMT) layered clay and epoxy resin (DEGBF). Two different techniques were used for dispersing the clay particles in the epoxy matrix, viz. high-speed shear dispersion and ultrasonic disruption. The volume fraction of clay particles was systematically varied from 0.5 to 6%, and mechanical properties, viz. flexural modulus and fracture toughness, were studied as a function of clay volume fraction and the processing technique. The flexural modulus was observed to increase monotonously with increase in volume fraction of clay particles, while, the fracture toughness showed an initial increase on addition of clay particles, but a subsequent decrease at higher clay volume fractions. In general, nanocomposites processed by shear mixing exhibited better mechanical properties as compared to those processed by ultrasonication. Investigation by X-ray diffraction (XRD) revealed exfoliated clay structure in most of the nanocomposites that were fabricated. Morphologies of the fracture surfaces of nanocomposites were studied using a scanning electron microscopy (SEM). Presence of river markings at low clay volume fractions provided evidence of extrinsic toughening taking place in an otherwise brittle epoxy.     

Biodegradable green composites made using bamboo micro/nano-fibrils and chemically modified soy protein resin

Micro/nano-sized bamboo fibrils (MBF) and a modified soy protein resin were used to fabricate environmentally friendly composites. With the incorporation of MBF the fracture stress and Young’s modulus of the soy protein concentrate (SPC) increased significantly. With the addition of 30 parts of MBF (SPC is 100 parts, based on weight), the fracture stress and Young’s modulus were increased from 20.2 MPa to 59.3 MPa and from 596 MPa to 1816 MPa, respectively. The addition of MBF, however, did not show significant decrease in the fracture strain of the specimens. As a result, the toughness of the MBF reinforced SPC increased. The toughness of the SPC based composites containing 30 parts of MBF was 6.0 MPa compared to 2.7 MPa for SPC without MBF. MBF reinforced SPC was then cross-linked using a silane, (3-isocyanatopropyl)triethoxysilane (ITES). Although the fracture strength and Young’s modulus did not show significant increase, the modification using ITES showed significant increase in the fracture toughness. SPC containing 30 parts of MBF, 10 parts of ITES and 2 parts of glycerol showed fracture stress of 82 MPa, Young’s modulus of around 3.2 GPa and toughness of 4.3 MPa. The environment-friendly, fully biodegradable green composites, based on MBF and modified SPC resins, have excellent properties and great potential to replace the traditional petroleum-based materials in many applications.     

Atomistic simulation of the mechanical behaviors of co-continuous Cu/SiC nanocomposites

In this paper, molecular dynamics (MDs) simulation was employed to investigate the mechanical behaviors of co-continuous Cu/SiC nanocomposites. The calculated results show the Young’s modulus and yield stress of the nanocomposites increase nonlinearly with the volume fraction (VF) of SiC. The Young’s modulus predicted by MD simulation is in good agreement with the micromechanics methods. The interfacial properties are found to play an important role in the plastic deformation of the nanocomposites. With the temperature increase, the co-continuous Cu/SiC nanocomposites show a brittle-to-ductile transition at about 700 K and the ultimate yield stress decreases linearly with the increase of temperature. This research is intended to give an insight into the mechanical behaviors of co-continuous nanocompoistes at an atomistic level.     

High temperature flexural strength and fracture toughness of AlN with Y<Subscript>2</Subscript>O<Subscript>3</Subscript> ceramic

The effects of temperature on the fast fracture behavior of aluminum nitride with 5 wt% Y₂O₃ ceramic were investigated. Four-point flexural strength and fracture toughness were measured in air at several temperatures (30–1,300 °C). The flexural strength gradually decreased with the increase of temperature up to 1,000 °C due to the change in the fracture mode from transgranular to intergranular, and then became almost constant up to 1,300 °C. Two main flaw types as fracture origin were identified: small surface flaw and large pores. The volume fraction of the large pores was only 0.01%; however, they limited the strength on about 50% of the specimens. The fracture toughness decreased slightly up to 800 °C controlled by the elastic modulus change, and then decreased significantly at 1,000 °C due to the decrease in the grain-boundary toughness. Above 1,000 °C, the fracture toughness increased significantly, and at 1,300 °C, its value was close to that measured at room temperature.     

Toughness indices of steel fiber reinforced concrete under mode II loading

The toughness indices of fiber reinforced concrete under Mode II loading effects are rarely reported due to lack of information on standard testing procedures. However, the direct shear test with improvement over JSCE-SF6 method is generally accepted to study Mode II fracture parameters. In this paper, experimental investigations to determine the fracture properties and toughness indices of steel fiber reinforced concrete (FRC) under Mode II loading are reported. Straight steel fibers of length 25 mm with an aspect ratio of 44.6 were randomly distributed in concrete with varying fiber volume fractions of 0, 0.5, 1.0 and 1.5%. A symmetrical Mode II loading set up was designed to achieve an ideal shear failure. It has been observed that the failure was due essentially to shear (Mode II) fracture without secondary flexural cracking. Plain concrete failed at a low equivalent shear strain of 0.5%, while the addition of steel fibers improved the shear strains up to as much as 8.0%. The shear strength and the shear toughness of concrete with the addition of steel fibers have been improved very significantly. As the volume fraction of fibers increases, the shear strength increases up to an optimum volume fraction, beyond which there has been no improvement on the shear strength. However, the toughness indices determined in Mode II loading (shear) have been observed to be about 15 times as high as that under Mode I loading (flexure).     

Metal fibre reinforced hydroxy-apatite ceramics

The reinforcement of hydroxy-apatite ceramics with metal fibres is discussed. Hastelloy X and FeCralloy fibres were dispersed in hydroxy-apatite powder slurry. The fibre-powder slurries were dried and sieved over a wide aperture sieve. The resulting granules were used for die pressing. Volume fractions used were 10, 20 and 30%. The compacts obtained in this way were isostatically repressed at 4 k bar. These compacts showed considerable strength and toughness. Hot-pressing of the compacts was done at about 1000'C and a pressure between 0.2 and 1.0 k bar for 15 min. The resulting materials were characterized by fractography and strength, fracture toughness, Young's modulus and hardness measurements. Both strength and fracture toughness increased while Young's modulus and hardness decreased with increasing volume fraction of fibres. The strength and fracture toughness of composites containing 20 vol % metal fibres showed an increase of the strength and fracture toughness by a factor of about 2 and 6, respectively, as compared with the strength of about 100 M Pa and a toughness of 1 .0 MPa m^1/2 for the sintered, pure matrix materials. The results obtained are also promising for other metal fibre-ceramic matrix composites.     

Effects of Si addition on microstructure and mechanical properties of Mg–8Gd–4Y–Nd–Zr alloy

Effects of Si addition (1.0 wt.%) on microstructure and mechanical properties of Mg–8Gd–4Y–Nd–Zr alloy have been investigated using scanning electron microscopy (SEM) equipped with energy dispersive spectrum (EDS), X-ray diffraction (XRD), hardness measurements and tensile testing. The results indicated that the addition of Si led to the formation of Mg₂Si and (RE + Si)-rich particles, which enhanced the Young’s modulus of the alloy by 7 GPa while decreased the yield strength and ultimate strength by 10 MPa and 31 MPa, respectively. The tensile properties of the Mg–8Gd–4Y–Nd–Zr–Si alloy are as follows: Young’s modulus E = 51 GPa, yield strength σ_0.2 = 347 MPa, ultimate strength σ_b = 392 MPa and elongation δ = 2.7%. The increase in Young’s modulus was attributed to the formation of particles with high Young’s modulus, while the decrease in strength was ascribed to the decrease in volume fraction of metastable β′ precipitates caused by the consumption of rare earth atoms due to the formation of the rare earth containing particles.