Análise do comportamento da madeira submetida a um ensaio de impacto inercial pelo método dos campos virtuais
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2018-11-30
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Neste trabalho foram identificadas propriedades elásticas da madeira da espécie Pinus pinaster Ait., em ensaios a elevadas taxas de deformação, utilizando o método dos campos virtuais. Nesse sentido foi usado um ensaio inercial de impacto. Experimentalmente, recorrendo a uma câmara digital ultra rápida, foram registadas imagens da deformação do provete em diversos instantes do ensaio dinâmico. Estas imagens foram posteriormente processadas pelo método das grelhas, de forma a obter dados quantitativos sobre os deslocamentos na superfície do provete em estudo. As deformações foram obtidas a partir de uma derivação espacial dos deslocamentos e as acelerações a partir de uma derivação temporal, de segunda ordem, dos deslocamentos. Com a utilização do método dos campos virtuais, foi possível identificar os parâmetros constitutivos do material, sem a necessidade de medição de forças externas aplicadas, utilizando a aceleração como célula de carga, tomando assim partido das forças inerciais, não desprezáveis, que estão presentes nos ensaios dinâmicos, ao contrário do que acontece em ensaios estáticos ou quase-estáticos. A metodologia foi validada com dados provenientes de simulações numéricas num material isotrópico e ortotrópico. No modelo isotrópico foi possível identificar todos os parâmetros constitutivos do material, numa pequena amplitude de erro. Por outro lado, no modelo ortotrópico, devido à maior complexidade, foi apenas possível obter um dos parâmetros constitutivos do material. Uma das possíveis causas baseia-se na falta de heterogeneidade e complexidade da configuração de ensaio utilizada na simulação, não conseguindo registar, por exemplo, o comportamento do material ao corte. Para melhorar os resultados obtidos, seria necessário modificar a configuração do ensaio utilizada, como por exemplo, utilizando ensaios fora dos eixos de simetria do material, possuindo assim uma maior heterogeneidade na resposta mecânica do material. Experimentalmente, foram realizados ensaios de impacto em provetes de madeira com duas orientações distintas: plano RT (Radial-Tangencial) e TR (Tangencial-Radial). Os dados experimentais foram utilizados para a identificação das propriedades do material em estudo. Numa primeira aproximação, foi utilizado um modelo isotrópico do método dos campos virtuais, uma vez que estes planos de orientação apresentam um baixo rácio de ortotropia. Os parâmetros identificados vão ao encontro de valores de referência para a espécie em estudo. No plano RT, o módulo de Young para condições dinâmicas foi em média superior em 5 % em relação ao valor homólogo quase-estático, enquanto que o coeficiente de Poisson foi inferior em 16 %. No plano TR, o módulo de Young em carregamento dinâmico foi em média inferior em 11 % relativamente a condições quase-estático, enquanto que o coeficiente de Poisson foi inferior em 37 %. Dada a variabilidade natural da madeira, estas percentagens não permitem, contudo, definir uma clara variação destes parâmetros elásticos do regime quase-estático para as condições dinâmicas. A sensibilidade do material ao efeito da taxa de deformação, a par de alguns materiais compósitos, poder-se-á notar mais ao nível do comportamento não linear e da tensão de rotura, cujos efeitos se poderão estudar em trabalho futuro.
In this work, elastic properties of Pinus pinaster Ait. wood were identified at high strain rate regimes using the virtual field method (VFM). The proposed approach is based on an inertial impact test coupled with an ultra high speed digital camera. The grid method was used for assessing the deformation of the specimens during the impacted loading. The displacement field was measured by processing the crossed grid images using a phase evaluation algorithm. On the one hand, the strain field was obtained from the spatial derivation of the displacement fields. On the other hand, the acceleration fields were reconstructed from a second order temporal derivative of the displacements. By means of the VFM, it was possible to identify the constitutive parameters of the material without the need to measure external forces, by using the acceleration as the load cell. This approach takes advantage of the non-negligible inertial forces that are present in the dynamic loading, contrasting with quasi-static testing. The methodology was firstly validated from numerical simulations in an isotropic and orthotropic material using the Explicit Dynamic module of ANSYS WORKBENCH. In the isotropic model it was possible to identify all the constitutive parameters of the material, although variable with the instant of time of the test duration. Secondly, an orthotropic model describing the macroscopic behaviour of wood in the longitudinal-radial plane was considered. In this configuration, however, only the Young modulus EL could be identified. One of the possible reasons can be based on the lack of heterogeneity and complexity of the test configuration used in the simulation, failing to record, for example, the shear behaviour of the orthotropic material. To improve the identifiability, it would be necessary to modify the test configuration, for example, using off-axis specimens, enhancing the complexity and heterogeneity of the mechanical response of the material. Experimentally, impact tests were carried out on wooden specimens with two different orientations: RT (Radial-Tangential) and TR (Tangential-Radial). The experimental data were used to identify the properties of the material. In a first approximation, an isotropic model of the VFM was used, since the anisotropic ratio of the material in the transverse plane is low (about 1.9). The identified parameters were in agreement with reference values for the species under study. In the RT plane, the Young modulus under dynamic conditions was in average 5% higher than the quasi-static counterpart, whereas the Poisson’s ratio was 16% less. In the TR plane, the Young Modulus in dynamic loading was on average 11% lower than quasi-static conditions, whereas the Poisson’s coefficient was 37% lower. Given the natural variability of wood, these percentages do not allow a clear statement about the variability of these elastic parameters from quasi-static to high strain rate regimes. The sensitivity of the material to strain rate effects, along with some composite materials, may be more noticeable in the nonlinear behaviour and on the tensile strength. These effects should be studied in future work.
In this work, elastic properties of Pinus pinaster Ait. wood were identified at high strain rate regimes using the virtual field method (VFM). The proposed approach is based on an inertial impact test coupled with an ultra high speed digital camera. The grid method was used for assessing the deformation of the specimens during the impacted loading. The displacement field was measured by processing the crossed grid images using a phase evaluation algorithm. On the one hand, the strain field was obtained from the spatial derivation of the displacement fields. On the other hand, the acceleration fields were reconstructed from a second order temporal derivative of the displacements. By means of the VFM, it was possible to identify the constitutive parameters of the material without the need to measure external forces, by using the acceleration as the load cell. This approach takes advantage of the non-negligible inertial forces that are present in the dynamic loading, contrasting with quasi-static testing. The methodology was firstly validated from numerical simulations in an isotropic and orthotropic material using the Explicit Dynamic module of ANSYS WORKBENCH. In the isotropic model it was possible to identify all the constitutive parameters of the material, although variable with the instant of time of the test duration. Secondly, an orthotropic model describing the macroscopic behaviour of wood in the longitudinal-radial plane was considered. In this configuration, however, only the Young modulus EL could be identified. One of the possible reasons can be based on the lack of heterogeneity and complexity of the test configuration used in the simulation, failing to record, for example, the shear behaviour of the orthotropic material. To improve the identifiability, it would be necessary to modify the test configuration, for example, using off-axis specimens, enhancing the complexity and heterogeneity of the mechanical response of the material. Experimentally, impact tests were carried out on wooden specimens with two different orientations: RT (Radial-Tangential) and TR (Tangential-Radial). The experimental data were used to identify the properties of the material. In a first approximation, an isotropic model of the VFM was used, since the anisotropic ratio of the material in the transverse plane is low (about 1.9). The identified parameters were in agreement with reference values for the species under study. In the RT plane, the Young modulus under dynamic conditions was in average 5% higher than the quasi-static counterpart, whereas the Poisson’s ratio was 16% less. In the TR plane, the Young Modulus in dynamic loading was on average 11% lower than quasi-static conditions, whereas the Poisson’s coefficient was 37% lower. Given the natural variability of wood, these percentages do not allow a clear statement about the variability of these elastic parameters from quasi-static to high strain rate regimes. The sensitivity of the material to strain rate effects, along with some composite materials, may be more noticeable in the nonlinear behaviour and on the tensile strength. These effects should be studied in future work.
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Dissertação de Mestrado em Mestrado em Engenharia Mecânica apresentada à Universidade de Trás-os-Montes e Alto Douro
Palavras-chave
Comportamento dinâmico , Método dos Campos Virtuais , Madeira , Elevadas taxas de deformação , Técnicas óticas de campo , Tecnologia de imagem ultra rápida