Laminate Thickness Research Articles

Numerical simulation and design method of dowel-type timber joints connecting laminated veneer lumber

Dowel laminated timber (DLT) is a structural engineering wood product composed of laminates connected by wood dowels. It has the characteristics of green, low-carbon, and a high degree of prefabrication. Wood dowel connection is the forming method of DLT, and its joint design is the key to DLT. The properties of laminates affect the mechanical properties of both DLT and dowel-type timber joints. Laminated Veneer Lumber (LVL) is an engineering wood product made by gluing veneers along a fixed grain direction, with excellent physical and mechanical properties. Utilizing small-thickness LVL as the laminates of DLT, a design method of dowel-type timber joints connecting LVL was explored through numerical simulation and theoretical calculation. A three-dimensional finite element model of dowel-type timber joints connecting LVL was presented, and experimental calibration were carried out. The parametric study was adopted to explore the influence of main variables on the shear performance of joints. The calculation formula for the shear capacity of joints was proposed and optimized, and the design method of joints was summarized. The results indicated that the failure mode and shear capacity of joints were dramatically influenced by two variables: the ratio of side laminate thickness to dowel diameter (n) and the thickness ratio of middle-to-side laminate (m). The two variables affected the shear capacity of joints by affecting the failure mode of joints. When the ratio of side laminate thickness to dowel diameter was 1 < n ≤ 3.75, the optimized Johansen theoretical formula could effectively predict the shear capacity of dowel-type timber joints connecting LVL.

Global Sensitivity Analysis of Factors Influencing the Surface Temperature of Mold during Autoclave Processing.

During the process of forming carbon fiber reinforced plastics (CFRP) in an autoclave, deeply understanding the global sensitivity of factors influencing mold surface temperature is of paramount importance for optimizing large frame-type mold thermally and enhancing curing quality. In this study, the convective heat transfer coefficient (CHTC), the thickness of composite laminates (TCL), the thickness of mold facesheet (TMF), the mold material type (MMT), and the thickness of the auxiliary materials layer (TAL) have been quantitatively assessed for the effects on the mold surface temperature. This assessment was conducted by building the thermal-chemical curing model of composite laminates and utilizing the Sobol global sensitivity analysis (GSA) method. Additionally, the interactions among these factors were investigated to gain a comprehensive understanding of their combined effects. The results show that the sensitivity order of these factors is as follows: CHTC > MMT > TMF > TCL > TAL. Moreover, CHTC, MMT, and TMF are the main factors influencing mold surface temperature, as the sum of their first-order sensitivity indices accounts for over 97.3%. The influence of a single factor is more significant than that of the interaction between factors since the sum of the first-order sensitivity indices of the factors is more than 78.1%. This study will support the development of science-based guidelines for the thermal design of molds and associated heating equipment design.

Morphometric Analysis of the Neural Arch of C2 Vertebra in Indian Population.

The most common injuries to upper cervical spine are fractures of the second cervical vertebrae. The study aims to evaluate the morphometry of the neural arch of the second cervical vertebrae in the South Indian population. Sixty-three second cervical vertebrae of undetermined gender and age without any gross defect were used for the study. The dimensions of neural arch, including superior articular facet, inferior articular facet, pediculoisthmic component, lamina, spinous process, foramen transversarium, and vertebral foramen, were measured by two independent observers using digital vernier caliper accurate to 0.1 mm and the data was analyzed. Descriptive statistics were obtained for the variables. Paired t-test was done to compare the measurements between right and left sides. There was no statistical difference between the right and left sides of the dimensions of superior articular facets, foramen transversarium, and the transverse diameter of inferior articular facet. The anteroposterior diameter of the inferior articular facets was more on the right side (P = 0.009). The width of the pediculoisthmic component in both the superior and inferior aspects was found to be less on the right side than that of the left (P = 0.006 and P = 0.031, respectively). The thickness in the middle one-third of laminae was optimum for bilateral safe screw insertion (≥4.0 mm) in 77% specimens. In summary, measurements of the transverse diameter of superior articular facet and thickness of lamina differed significantly from those reported in literature. This should be kept in mind while doing neurosurgery procedures in the Indian population.

Experimental and numerical investigation of preloaded recycled concrete beams strengthened with CFRP

Purpose The use of recycled coarse aggregate in concrete structures promotes environmental sustainability; however, performance of these structures might be negatively impacted when it is used as a replacement to traditional aggregate. This paper aims to simulate recycled concrete beams strengthened with carbon fiber-reinforced polymer (CFRP), to advance the modeling and use of recycled concrete structures. Design/methodology/approach To investigate the performance of beams with recycled coarse aggregate concrete (RCAC), finite element models (FEMs) were developed to simulate 12 preloaded RCAC beams, strengthened with two CFRP strengthening schemes. Details of the modeling are provided including the material models, boundary conditions, applied loads, analysis solver, mesh analysis and computational efficiency. Findings Using FEM, a parametric study was carried out to assess the influence of CFRP thickness on the strengthening efficiency. The FEM provided results in good agreement with those from the experiments with differences and standard deviation not exceeding 11.1% and 3.1%, respectively. It was found that increasing the CFRP laminate thickness improved the load-carrying capacity of the strengthened beams. Originality/value The developed models simulate the preloading and loading up to failure with/without CFRP strengthening for the investigated beams. Moreover, the models were validated against the experimental results of 12 beams in terms of crack pattern as well as load, deflection and strain.

Neural networks modeling of strain energy density and Tsai-Wu index in laminated composites

In laminated composite materials design, optimization mainly targets the stacking sequence configuration, which is defined by the lamina thickness and fiber orientations within each layer. Recent studies emphasize the increasing role of Machine Learning in promoting innovative composite designs by facilitating the accurate modeling of essential properties such as strength and stiffness. This study introduces two metamodels that utilize feed-forward artificial neural networks, taking laminate thickness and fiber steering angles as input parameters. The output variables, including strain energy density and the Tsai-Wu failure index, enable the prediction of stacking sequence configurations for laminated materials, a capability confirmed in a case study. The results showcase neural network models with the ability to predict these variables, achieving coefficients of determination above 0.90 for testing data. Consequently, this modeling approach has the potential to be a tool for designers, aiding in decision-making processes for the subsequent optimization of stiffness and strength in structural components made of laminated composite materials.

Ballistic impact modeling of woven composites using the microplane triad model with meso-scale damage mechanisms

Existence of undulating fill and warp yarns in woven composite laminae introduces complex unit cell geometries and multi-scale interactions among the constituents. Due to these, the failure process involves various meso-scale constituent-level failure modes under complex loading scenarios such as ballistic impact. This can be challenging to model via conventional macro-scale damage tensor-based models. This challenge is tackled here via the adaptation of the previously developed multi-scale microplane triad model to ballistic impact of woven composites. The model can resolve meso-scale constituent level details (including yarn undulations) and predict not only the elastic constants of a woven lamina but also its fracturing behavior. In the present adaptation, only two damage laws are formulated, one for the fibers and one for the matrix. This enables the model to embody the correct values of the intralaminar mode I and II fracture energies of the woven lamina. The model is calibrated using constituent and lamina level test data, and then used to predict the ballistic impact behavior of a single plain-woven lamina under a wide range of projectile impact velocities. The model is demonstrated to predict very well the projectile residual (rebound and exit) velocities, the energy dissipation, the major failure modes of the lamina and the corresponding extent of damage, as well as the ballistic limit and deformation cone wave propagation speeds. The model’s simple, conceptually clear architecture, and computational efficiency represent a major advantage compared to existing damage tensor-based models. The model is also extended to multi-layer thick section woven laminate impact, where the analyses consider both intralaminar and interlaminar failures. The predictions are found to be comparable to those from MAT162, a commercially available material model in LS-Dyna, with much better computational efficiency. Via detailed sensitivity studies, it is demonstrated that the mode I and II intralaminar fracture energies of the lamina are a crucial model input, necessary for accurate predictions of ballistic impact. Not knowing these can introduce significant uncertainty and therefore, their characterization is an absolute must. Finally, the optimal meshing considerations as well as the advantages and limitations of the microplane triad model are discussed.

Morphological characterization of newly developed orangelo (Citrus spp.) hybrids

Present study was carried out during 2021–23 (Ambe and Mrig bahar season) at the research farm of ICAR- Indian Agricultural Research Institute, New Delhi to analyse the morphological diversity of 24 orangelo (Citrus spp.) hybrids and their 4 parents based on 17 quantitative traits such as leaves, flowers, fruits and seed characters. Cluster analysis based on 17 morphological traits divided 28 genotypes of citrus into two main groups. A higher range of variation with average Euclidean distance coefficients ranging from 0.02–0.26 was observed between groups as well as clusters, thereby indicating that genotypes within and among clusters were highly diverse. The PCA for morphological quantitative traits showed that five components leaf lamina length (LLL); leaf lamina width (LLW); LLL: LLW; leaf lamina thickness and pedicel length, of the 17 principal component axis had Eigen-values&gt;1 and all together accounted for over 77.76% of the total variability. Analysing the genetic relationships among the hybrids yielded important insights for potential use in future breeding programmes as valuable sources of desirable traits.

Influence of fibre orientation parallel to impact direction on the impact response of unidirectional glass/epoxy composite: Experimental investigation on confinement and hybridisation

In a high-velocity impact phenomenon, the damage is localised, and for thick composite laminates, most of the projectile’s kinetic energy is absorbed through out-of-plane compression and shear mechanisms. In conventional composite laminate, as the fibre orientations are in the in-plane of laminate, the out-of-plane compression and out-of-plane shear of laminate are utilised. In composites, the out-of-plane compressive strength is significantly lower than the in-plane (fibre direction) strength. The present study investigates the impact response of unidirectional (UD) glass/epoxy composite targets with fibres oriented parallel to the impact direction. The lack of research on the impact behaviour of unidirectional glass/epoxy composites with fibre orientation parallel to the impact direction demands further experimentation and understanding of failure mechanisms. In this study, firstly, the impact response of UD glass/epoxy composites with fibres oriented parallel to the impact direction (GFID) was investigated and compared with conventional cross-ply (GFCP) and quasi-isotropic (GFQI) glass/epoxy laminates. Secondly, to address the issues of GFID splitting on impact, GFID was confined in both the hoop and normal-to-binder directions. Thirdly, the impact response of various hybrid GFID with and without confinement with GFCP as backing was evaluated. GFID under out-of-plane punch load fails by splitting, and its compressive participation depends on the impact velocity. GFID under the hoop and normal-to-binder direction confinement showed better specific impact energy absorption relative to pure GFID. The experimental results show that GFID wounds with carbon fibre used as a facing with GFCP as a backing provide better impact resistance at HVI conditions than conventional laminates of the same thickness. These findings suggest that the combination of GFID and GFCP targets can be used to have better impact resistance in various applications.

Effects of the Injection Material and Resin Layer on the Mechanical Properties of Carbon Fiber-Reinforced Thermoplastic (CFRTP) Press and Injection Hybrid Molded Parts

In the press and injection hybrid molded parts of fiber-reinforced thermoplastics (FRTPs), failure at the interface between the surface material (the outer shell) and the ribs (the injection part) or that at the injection part has become an issue. Adding a resin layer to the rib roots at the same time that the ribs are molded through injection has been proposed, which may increase the mechanical properties and reduce the material cost. To prevent failure at the injection part, the use of fiber-reinforced resin as an injection material has been suggested. This approach contributes to a higher bond strength by lowering the molding shrinkage rate. In this study, the hat-shaped parts of carbon fiber-reinforced thermoplastics (CFRTPs) with fiber-reinforced and neat resin layers at the rib root were fabricated through press and injection hybrid molding, and their mechanical properties were evaluated through three-point bending tests. The effects of the resin layer at the rib root and the existence or nonexistence of fiber reinforcement on the mechanical properties, as well as the relationship between the material cost and the mechanical properties, were clarified through an experiment and FEM analysis. The bond strength was also evaluated through tensile tests that were undertaken at the rib root. Molded parts with neat PA6 and glass fiber-reinforced PA6 resin layers at the rib roots showed higher bond strength than those without resin layers. In a three-point bending test of a CFRTP hat-shaped part with a resin layer at the rib roots, the use of a 1 mm thick CFRTP laminate for the outer shell and glass fiber-reinforced PA6 resin as the injection material showed the same stiffness as a part that used a 2 mm thick CFRTP laminate for the outer shell. FEM analysis showed that the resin layer prevented the concentration of strain at the rib roots, and the model that used a 1 mm thick CFRTP laminate for the outer shell and glass fiber-reinforced PA6 resin as the injection material showed the best specific stiffness in this study. By adding a resin layer to the rib roots, the fabrication of molded parts with excellent specific stiffness was enabled at a small increase in cost.

Ultrasonic imaging of delamination in thick CFRP laminates using an energy-compensation reverse time migration method

In ultrasonic reflection method, the precision of defect detection in thick carbon fiber reinforced plastics (CFRP) is compromised by acoustic energy attenuation. An energy-compensation reverse time migration (ECRTM) method is proposed to identify multiple defects accurately. Forward and backward wavefields are formed using the finite element method within an anisotropic acoustic model based on the Christoffel equation and Bond transformation. To enhance the imaging quality of CFRP laminates, a novel cross-correlation imaging condition is introduced to compensate for energy dissipation caused by geometric diffusion and variations of the far-field radiation intensity at the emitter with the propagation direction. Employing ultrasonic detection technology with a multi-element array, numerical and experimental research on defect imaging was conducted, considering delamination with various sizes and positions in a multidirectional CFRP laminate. In comparison to other ultrasonic imaging methods, the near-surface artifacts in RTM images are mitigated by the far-field radiation directivity factor, while the deep information is enhanced by the geometric diffusion compensation factor in the ECRTM images. As a result, the precise position of delamination in CFRP laminates is achievable, demonstrating superior imaging capabilities, especially for deep delamination.

Evaluation of Five Chrysanthemum morifolium Cultivars against Leaf Blight Disease Caused by Alternaria alternata at Rooting and Seedling Growth Stages.

During the winter of 2018, leaf blight on florist's daisy (Chrysanthemum morifolium L.) was noticed in Egypt. The disease, which was identified as caused by Alternaria alternata, was widely spread and led to serious damage for the exportation sector of this crop. Therefore, a study was conducted to better understand what can be conducted to minimize the problem in the future. Isolates were gathered and evaluated on five chrysanthemum cultivars (i.e., 'Feeling Green Dark', 'Talitha', 'Chrystal Regan', 'Arctic queen', and 'Podolsk Purple') grown in a greenhouse. The objectives were to isolate and identify the phytopathogen and detect the resistant degree of these cultivars with emphasis on the early growth stages of the crop. The results showed that 'Podolsk Purple' was the most resistant cultivar against the different isolates during the rooting and seedling growth stages. 'Chrystal Regan' was very susceptible to the different isolates. In addition, the isolate from 'Feeling Green Dark' was the strongest, which negatively affected the chlorophyll content and its fluorescence parameters besides other measured vegetative and anatomical features. The findings indicated that the best anatomical characters of the stem and leaf, like the thickness of cuticle and cortex, stem diameter, xylem vessel diameter, and thickness of epidermis as well as lamina thickness were recorded in the 'Podolsk Purple' cultivar. This study highlighted that by using the right cultivars, chrysanthemum can be cultivated during the winter season under Egyptian conditions. These results can be a part of solution to overcome the leaf blight caused by A. alternata on chrysanthemum during the early growing stages.

A simple recovery post-processing of stresses and displacements in Reissner–Mindlin analysis of anisotropic laminated plates

The bending problem of anisotropic laminated plates is considered, modeled with first order shear deformation (FSDT) kinematic model and approximations obtained from the Generalized Finite Element Method (GFEM/ XFEM). A procedure is developed to recover the transverse normal and shear stresses and all displacement components, with improved variations across the laminate thickness, generating a complete three-dimensional approximate solution of the problem. The procedure starts with the results issuing from direct computations of in-plane stresses and displacements obtained by the 2D kinematic and constitutive equations. The recovered fields are obtained to, approximately, enforce local equilibrium, constitutive and strain–displacement equations in their three-dimensional forms, and interlaminar continuity. The general procedure considers inertia forces and von Kármán non-linearity. Corrections are made to impose the necessary 3D boundary conditions in both faces of the laminate. The easy way the GFEM admits basis function enrichment, whether by singular, discontinuous or by higher order p-enrichment, on a fixed mesh, makes the entire recovery procedure straightforward and non-iterative. The recovered fields accuracy is demonstrated in standard problems against exact solutions from three-dimensional elasticity and FEM reference approximations. Up to the author’s knowledge, the presented strategy is novel in the published literature of non-iterative post-processing methods. It provides a simple mean to obtain all stress and displacement component approximations necessary to application in many complete 3D local failure theories.

Evolution of Through-Thickness Texture and Microstructure of an ARB-Processed Nb1-Zr Alloy

AbstractThis study investigates the effects of accumulative roll bonding processing on a commercial Nb1Zr alloy. The sheets were subjected to preheating, followed by five reduction cycles. Microstructural evolution was examined through metallography, revealing increasing homogenization of the morphology across the laminate thickness. Microhardness increased from 109 HV to 187 HV in the final laminate due to grain refinement. Electron back-scattered diffraction analysis showed removal of shear strain effects with each deformation step, highlighting microstructural heterogeneity and texture variation. The Goss texture was intensified at the surface during the third cycle, attributed to surface recrystallization. Low-angle grain boundaries were prevalent initially, shifting to a bimodal distribution favoring high-angle grain boundaries with increased deformation, linked to dynamic recovery and recrystallization.

Numerical and experimental comparison of the no-load losses in the different grain-oriented electrical steel materials

One of the critical pieces of equipment for power transmission and distribution is the transformer. The operation of the transformers is essential for the power supply's continued stability and efficacy. With an increase in rated power, the transformer's manufacturing time, cost, and size all go up. The core loss of the transformer is still a big concern for transformer designers. Minimization of the core loss in the transformer is also important for transformer manufacturers. Accurate evaluation of the core loss is also important for optimizing the magnetic design of the transformer. Evaluating the no-load losses of the new magnetic materials also needs a reliable technique as conventional analytical methods are limited and difficult to implement. In this study, the use of different materials for manufacturing the core of the transformers is used to minimize and compare the no-load losses. In this work, different types of grain-oriented silicon steel and lamination thickness are used for core materials to evaluate and minimize the core losses using numerical analysis. The results of the two different materials are also verified by a no-load experiment test performed on the prototype transformers. Considering the finite element analysis results of the different materials, core losses were calculated as 66.35 % lower in the M-H0 material than in the reference M-6 material. To increase transformer efficiency, a material with low no-load losses can be used. The results of this work will give guidelines to the transformer designers for selecting core materials to improve the efficiency of the transformer.

Experimental and Numerical Study of CFRP Laminate Strengthened Concrete Beams Under Hygrothermal Environment

Carbon fiber reinforced polymer (CFRP) laminates are widely used to strengthen and retrofit deteriorated concrete structures, yet their long‐term performance and durability under varied environmental conditions remain critical areas of investigation. This study comprehensively examined the behavior of small concrete beams externally bonded with CFRP laminates under three distinct hygrothermal regimes: immersion in water at 23, 45, and 60°C for up to 112 days. The experimental program encompassed direct tension pull‐off testing of the CFRP–concrete assembly and four‐point bending tests on the beams. Pull‐off tests revealed complex failure modes, with bonding epoxy failure (43%) and concrete substrate cohesion failure (39%) being dominant. Notably, pull‐off strength exhibited nonmonotonic trends across all environments, suggesting that environmental degradation is not solely time‐dependent. Flexural capacity increased by 20%, 49%, and 11% for room temperature (RT), moderate temperature (MT), and high temperature (HT) conditions, respectively, after 112 days, highlighting the synergistic effect of CFRP strengthening and ongoing concrete curing. A calibrated three‐dimensional finite element model, developed using Abaqus, accurately replicated the experimental results and facilitated parametric studies on factors influencing CFRP‐strengthened beam performance. This included concrete compressive strength, number of CFRP layers, laminate thickness, and FRP type. The study elucidates the complex interplay between environmental exposure, material properties, and structural performance, contributing valuable insights for enhancing durability predictions and design guidelines for CFRP‐strengthened concrete structures in diverse climatic conditions.

Mechanical Behavior of GFRP Composite Under Different Strain rates and Laminate Thicknesses

Mechanical Behavior of GFRP Composite Under Different Strain rates and Laminate Thicknesses

Durability of GFRP Composites Produced by Pultrusion under Thermal Environments

Fibre-reinforced polymer (FRP) composites have gained popularity in civil structural applications due to their advantages over traditional materials. Despite their proven better performance in harsh conditions, FRP composites are susceptible to degradation due to various environmental agents; moreover, the lack of durability data for relatively thick laminates produced by pultrusion is a concern. To address this, in the scope of the Durable-FRP project, an extensive experimental program was conducted to assess the durability of thick FRP laminates produced by pultrusion, consisting of glass fibres and unsaturated polyester and vinyl ester resin matrices, subjected to accelerated laboratory ageing and in-situ natural weathering. This paper presents preliminary results from durability tests on such glass-FRP (GFRP) laminates under particular thermal ageing environments, including constant temperatures of -15 °C, 20 °C, 40 °C, and 60 °C for a period over 12 months, as well as 100 and 200 thermal cycles between -15 °C and 60 °C. Following environmental exposure, the degradation of mechanical properties was evaluated using various tests, including tension (in both longitudinal and transverse directions), compression, flexure, in-plane shear, and interlaminar shear. In general, minor mechanical degradation was observed, except in terms of transverse tensile strength (resin-dominated) following constant exposure to extreme temperatures, with minimum property retentions of 74% and 83% at -15 °C, for vinyl ester and unsaturated polyester matrices, respectively.

Comparison of Inner Fitness of Crown Prosthesis Manufactured by 3D Printers Based on Lamination Thickness

Comparison of Inner Fitness of Crown Prosthesis Manufactured by 3D Printers Based on Lamination Thickness

Surface-Wetting Characteristics of DLP-Based 3D Printing Outcomes under Various Printing Conditions for Microfluidic Device Fabrication.

In recent times, the utilization of three-dimensional (3D) printing technology, particularly a variant using digital light processing (DLP), has gained increasing fascination in the realm of microfluidic research because it has proven advantageous and expedient for constructing microscale 3D structures. The surface wetting characteristics (e.g., contact angle and contact angle hysteresis) of 3D-printed microstructures are crucial factors influencing the operational effectiveness of 3D-printed microfluidic devices. Therefore, this study systematically examines the surface wetting characteristics of DLP-based 3D printing objects, focusing on various printing conditions such as lamination (or layer) thickness and direction. We preferentially examine the impact of lamination thickness on the surface roughness of 3D-printed structures through a quantitative assessment using a confocal laser scanning microscope. The influence of lamination thicknesses and lamination direction on the contact angle and contact angle hysteresis of both aqueous and oil droplets on the surfaces of 3D-printed outputs is then quantified. Finally, the performance of a DLP 3D-printed microfluidic device under various printing conditions is assessed. Current research indicates a connection between printing parameters, surface roughness, wetting properties, and capillary movement in 3D-printed microchannels. This correlation will greatly aid in the progress of microfluidic devices produced using DLP-based 3D printing technology.

Ballistic performance of bio-inspired hybrid interleaved composite structures suitable for aerospace applications

We investigate the ballistic performance of an aircraft engine containment casing demonstrator, made of composite materials with a novel bio-inspired hybrid interleaved design, under high-velocity impact (HVI) at a specific angle. Firstly, we apply a bio-inspired (BI) helicoidal design to develop a large-scale monolithic laminate concept made of carbon fibre-reinforced polymer (CFRP). Then, we hybridise the developed BI laminate concept with interleaved blocks of Zylon fibre (PBO)-reinforced polymer to develop a large-scale BI hybrid interleaved laminate concept. We then further hybridise the developed BI hybrid concept with titanium (Ti) foils (located at the impact face) so that in total we have three large-scale laminate concepts. We manufacture 6 large-scale laminates from each concept with dimensions of 225 × 225 mm and a target areal weight of 0.95 g/cm2. We then test them (perpendicularly) under HVI ranging from 150 to 300 m/s to obtain the ballistic limit and energy dissipation. Secondly, after selecting the best-performing developed laminate concept, we scale it up to develop industrial demonstrator panels with a target areal weight of 1.5 g/cm2 and dimensions of 550 × 360 mm. We test the panels under HVI at an angle of 55° with a larger and heavier projectile, to more closely represent a fan blade-off event onto the engine casing. The results of the large-scale laminate concept tests show that the BI hybrid interleaved CFRP/PBO concept outperformed the rest of the concepts with 54% and 34% improvement in energy dissipation compared to that of quasi-isotropic (QI) and the BI monolithic CFRP, respectively. Our results show that small-scale designs for HVI-resistant CFRP-based laminates cannot be simply assumed to exhibit an equivalent performance for industrial applications with thicker laminates, heavier projectiles and impacts at an angle.