simulation of residual stress in curved glulam beams - Engineered ...

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The thickness of glueline is neglected due to the fact that glueline is only a tiny part of Glulam, and the typical thickness is only 0.076-0.152mm [6]. The thickness of glueline is very minor compared with the dimensions of Glulam members. Thus, the thickness of glueline is neglected in the FE modelling. But the bond performance of adhesive in glueline is still considered. The bond performance is different in different stages of manufacturing. In the stage of forcing the laminas into the curved shape, the glue is still a liquid. It has no bond effect and can also reduce the friction between laminas. While when the adhesive is solidified, the bond effect is acquired. Laminas can neither slip relatively nor separate even when the pressure is removed. The deformation is so restrained that a curved Glulam beam is completed. Thus remains the residual stress. Because of the tiny thickness of glueline, the dimension of glueline is neglected in FE model. The bond performance of adhesive is considered through the frictional behaviour and separating behaviour in FE modelling-when the adhesive is liquid, the coefficient of friction is chosen as a small value and separating between laminas is allowed; when the adhesive is solidified, the coefficient of friction is chosen as a large value (rough friction) and separating between laminas is prevented. The material of Glulam is considered as an orthotropic material. For a two-dimensional problem, the plane stress relationship is ⎡ 1 υ12 ⎤ ⎢ − 0 ⎥ E1 E1 ⎧ε1 ⎫ ⎢ ⎥⎧σ11⎫ ⎪ ⎪ ⎢ υ12 1 ⎥⎪ ⎪ ⎨ε2 ⎬= ⎢− 0 ⎥⎨σ22⎬ (1) ⎪ E1 E2 γ ⎪ ⎢ ⎥⎪ 12 τ ⎪ ⎩ ⎭ ⎢ 12 1 ⎥⎩ ⎭ ⎢ 0 0 ⎥ ⎢⎣ G12 ⎥⎦ where 1 E , 2 wood; 12 G is the modulus of shear; υ 12 is Poisson’s ratio; E are the moduli of elasticity (MOE) of σ 11 , σ 22 and τ 12 are the stress components; ε 11 , ε 22 and γ are the strain components. 12 3 NUMERICAL SIMULATION OF STRESSES INDUCED FROM MANUFACTURING 3.1 MANUFACTURING PROCEDURE The process of manufacturing curved Glulam beams is as follows. The laminas sprayed with an adhesive are pressed on a rigid mould with designed curvature, and the pressure by applying external forces is kept until the designed strength of adhesive is reached. Then the external forces are removed, the curved shape can be retained due to the effect of bond. The procedure can be divided into two stages in FE modelling. Stage 1, to press the stacked laminas into the designed curve; Stage 2, to release the pressure after solidification of the adhesive between laminas. In stage 1, the coefficient of friction between laminas is reduced by the liquid adhesive. However, there is still some friction that depends on the craftsmanship like adhesive applying (spraying/brushing) and the type of the adhesive. Because of the different solidification times of adhesive, different coefficients of friction occurs in Stage 1. The coefficient of friction is thus taken as an important factor. In Stage 2, the curved beam is released from pressure after the adhesive is entirely solidified, and the strength of adhesive reaches such an extent that relative slippage between laminas is prevented, unless failure of glueline happens. Therefore, the rough friction between laminas is considered in the Stage 2, i.e. neither relative slippage nor separation between laminas takes place. 3.2 DETAILS OF THE CURVED BEAMS AND THE FE MESH Figure 1 shows a sketch for manufacturing a curved Glulam beam, which is made of 15 laminas. The crosssection of the curved Glulam beam is 90mm×180mm, and the cross-section of each lamina is 90mm×15mm with a length of L=3.2m. The species of wood is Chinese larch, the density is 580kg/m 3 , the MOE is 12000N/mm 2 , the modulus of shear is 400 N/mm 2 , the Poisson’s ratio is 0.42. The designed radius of curvature of the neutral axis is 5.0m. Therefore, the radius of curvature of the rigid mould is R=4.91m. The magnitude of pressure is p=0.5MPa. Making use of the symmetry, a half of the beam is modelled in the FE analysis. On the symmetrical face, there is no horizontal displacement and rotation. Each lamina is meshed with 5mm×5mm CPS4R element [7]. The coefficient of friction between wood is 0.3-0.5 [6]. In Stage 1, the coefficient is set as 0.1 due to the fact that the liquid adhesive decreases the friction. The rigid mould is considered as smooth, because the mould is actually discrete in practice. The residual stress distribution and the rebounding deformation during manufacturing of the curved Glulam beams are discussed as follows. Symmetry R p L/2 Rigid mould Figure 1: Sketch of manufacturing a curved Glulam beam P h Figure 2 shows the longitudinal stress distribution in the mid-length of a curved Glulam beam after the pressure is removed. In Stage 1, when the adhesive is liquid, the laminas can slip relatively. There is no composite action between laminas. Thus all laminas bend alike. When the adhesive is solidified, there is no relative slippage between laminas even when the pressure is removed. Therefore the entire composite action comes into being. In general, the longitudinal residual stress in the middle part of beam is larger than that around the free end. The stress in the top and the bottom of each lamina is the
largest due to the bending, with a representative value of about 13.1MPa for tension at the top and 12.9MPa for compression at the bottom. Thus, the distribution of longitudinal residual stress exhibits a saw-toothed shape. In the process of manufacturing, the largest longitudinal stress is about 13.1MPa, which occurs in bottom lamina due to most severe bending. Depth (mm) 90 0 -15 0 15 -90 Longitudinal residual stress (MPa) Figure 2: Longitudinal residual stress distribution at the mid-length of the curved Glulam beam Also in Stage 1, when the laminas are bent into a curve, there is compression between them. The compressive stress perpendicular to grain remains when the pressure is removed in Stage 2. The stress is all compressive except for where in the vicinity of glueline at the end of the beam, as indicated in Figure 3, which shows the local distribution of stress perpendicular to grain at the end of the beam. When the glue is hardened and the applied pressure is removed, the laminas in the upper part of the beam tend to rebound and are restrained by the neighbouring laminas below, thus giving rise to tensile stress between laminas at the end of the beam. The largest tensile stress perpendicular to grain at the end cross-section is about 0.16Mpa, while the largest compressive stress perpendicular to grain is 0.085MPa. In the mid-length the compression is about 0.04MPa. Figure 3: Residual stress perpendicular to grain at the free end of the curved Glulam beam The rebounding of a curved Glulam beam is also of concern. Figure 4 shows the deflection of Point P versus the pressure applied in the process of manufacturing. The maximum deflection, 248.6mm, occurs when the pressure reaches the maximum. When the pressure is removed completely, the amount of rebounding deformation is 4.9mmm, leaving a deflection of 243.7mm remained. The rebounding is only 1/635 of the length of beam, a very small portion of the dimension of the curved Glulam beam. The rebounding deformation, which reflects the difference between the designed curve and the curve in manufacturing, is an important factor to guide the setting up of the mould. Pressure (MPa) 0.5 0.4 0.3 0.2 0.1 0.0 0 50 100 150 200 250 Deflection of point P (mm) Figure 4: Rebounding of the beam 4 FACTORS AFFECTING THE RESIDUAL STRESS The residual stress in a curved Gulam beam is affected by factors such as the magnitude of pressure, radius of curvature of the neutral axis of beam, thickness of lamina and the time between applying the adhesive and applying the pressure to force the beam into the curved shape, as reflected by the coefficient of friction in Stage 1. The effect of these factors will be discussed through an example of simulating the manufacturing of a curved Glulam beam with a cross-section of 90mm×180mm. In order to investigate the effect, some parameters are prescribed in Table 1. Table 1: Parameters for manufacturing the curved Glulam beam Parameter Unit Value Radius of curvature R m 3.0 4.0 5.0 Pressure p MPa 0.5 0.75 1.0 Thickness of lamina t mm 15 20 30 45 Coefficient of friction µ 0.05 0.1 0.3 0.5 Figure 5 shows the effect of different parameters on the residual stress perpendicular to grain in the curved Glulam beams. As a general trend, the residual stress perpendicular to grain increases with the coefficient of friction that increases with the time interval between adhesive applying and pressure applying. This indicates that the sooner the process of Stage 1 in the manufacture, the less the stress in a curved Glulam beam. It can also
Page 1: SIMULATION OF RESIDUAL STRESS IN CU
Page 5 and 6: Longitudinal residual stress (MPa)

simulation of residual stress in curved glulam beams - Engineered ...

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