The methods currently used for predicting static fracture of notched composite laminates in tension, such as the point and average stress criteria and the inherent flaw criterion, are of semi-empirical nature and have limited applicability with respect to size and shape of the notch. In this paper, a damage zone analysis, based on more fundamental concepts, is used to predict fracture of laminates with circular holes of various radii, and oval and rectangular holes of various sizes. The damage is represented by a linear cohesive zone. Based on the two fundamental parameters unnotched tensile strength (σ 0 ) and apparent fracture energy (G* c ), this model excellently predicts the strength of notched laminates for a number of specimens tested.
In this paper a method, called the Damage Zone Model (DZM), is used for predicting strength of composites with through-the-thickness cracks. The DZM is based on the two fundamental parameters unnotched tensile strength (σ 0 ) and apparent fracture energy (G* c ). The damage zone, developed at a notch in the composite, is modelled as a crack with cohesive forces acting on the crack surfaces. Redistribution of stresses and change in stiffness is accounted for in the model. For comparison, strengths are also calculated by semi-empirical methods such as the inherent flaw and the point stress criteria.Experimental results for three point bend (TPB), single edge notch (SEN) and compact tension (CT) quasi-isotropic carbon/epoxy specimens are presented. Some results for specimens made from randomly oriented short glass fiber/polyester specimens are also discussed. The damage zone model is shown to accurately predict fracture load, loaddeformation behaviour and damage zone sizes in these types of laminates.
For trials exhibiting within-field spatial variability, good predictions of genetic nnerit require models that accurately estimate and partition spatial effects fronn genetic sources of variation. Ideally such models should be robust, providing good solutions across a range of spatial patterns. To achieve this, a new method for spatial corrections is proposed, which utilizes two-dimensional spline (2DS) interpolation to estimate spatial effects. Simulation experiments were used to compare this method with twodimensional separable autoregressive models (AR1) and mixed models containing marginal pass and range effects (PRM). Models were evaluated based on accuracy in partitioning genetic and spatial sources of variation as well as robustness across different spatial and genetic effect structures. Results showed the 2DS method to be the most robust of the three methods, yielding accurate spatial corrections across all simulation scenarios, wiiereas the AR1 model showed indications of over-fitting in the presence of genotype x environment interactions and the PRM model performed poorly in the presence of pass x range interactions. Applications using maize {Zea mays L.) inybrid yield and moisture data confirmed the effectiveness of the 2DS method at reducing the error variance by accounting for spatial trends. This new model provides breeders with a robust method to model within-field spatial variability across a range of experimental designs and spatial effect distributions. Dow AgroSciences LLC, 9330 Zionsville Rd., Indianapolis, IN 46268. Received 10 Aug. 2011. ^Corresponding author (krrobbins@dow.coni).Abbreviations: 2DS, two-dimensional spline; AD, augmented design; ARl, two-dimensional, separable autoregressive model; GE, genotype X environment interaction effects; MAD2, modified augmented design Type 2; PRM, marginal pass and range effects; RCBD, randomized complete block design. E NVIRONMENTAL EFFECTS play a huge role in the expression of complex plant phenotypes. For the accurate evaluation of genetic merit, the proportion of the phenotypic expression attributable to environment must be accurately partitioned from tbat attributable to genetics. This can be particularly challenging when modeling within-field spatial variability. Several trial designs have been developed to deal with spatial effects through blocking or systematic placement of standard test lines, and in the area of spatial analysis, several methodologies have been developed and investigated. Linear variance (Williams, 1986; Williams et al., 2006), autoregressive (Gleeson andCullis, 1987;Cullis and Gleeson, 1991), and moving-block nearest-neighbor approaches (Wilkinson et al., 1983) have been shown to give good performance in capturing spatial variation; however, little consideration has been given to how well the spatial effects are partitioned from the true genetic effects. This is of particular concern for trials with unreplicated entries within location, where localized spatial effects could be confounded with genetic and genotype X environ...
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