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Publication Number: FHWA-HRT-04-097
Date: August 2007
Measured Variability Of Southern Yellow Pine - Manual for LS-DYNA Wood Material Model 143
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Section 1. THEORETICAL MANUAL
This section documents the theory of the wood material model in detail. It begins with an overview of wood behavior, followed by an overview of the formulation. Then detailed equations are provided for each feature of the model (elasticity, plasticity, hardening, damage, and rate effects). Data are also tabulated for southern yellow pine and Douglas fir that are needed to fit the model parameters. Throughout this report, numerous figures, particularly those of test data, are reproduced from the various references cited at the end of each caption.
1.1 BEHAVIOR OF WOOD
Wood is a variable material; however, certain trends are evident. Stiffness and strength properties vary as a function of orientation between the longitudinal, tangential, and radial directions. Figure 1 helps to illustrate this point. The longitudinal direction is the fiber or grain direction. Stiffness and strength are greatest in the fiber direction. The tangential and radial directions are transverse to the fiber direction, and tangential and perpendicular to the growth rings. For modeling purposes, the distinction between the tangential and radial directions is not always significant. Therefore, this manual uses the term perpendicular to the grain when no distinction is made between the radial and tangential directions, and parallel to the grain to describe the longitudinal direction.
Wood material properties vary with orientation. The wood material coordinate system does not necessarily coincide with the board coordinate system.
Source: American Society of Civil Engineers.(6)
Loading wood at angles to the grain has a significant effect on strength, as demonstrated in figure 2 for Douglas fir. The data are indicated by the dots. Hankinson’s formula is indicated by the surface. This formula is discussed in section 1.4.
Ultimate tensile strength of Douglas fir measured in off-axis tests drops rapidly as the load is oriented at increasing angles to the grain.
Source: Society of Wood Science and Technology.(7)
The failure modes and measured stress-strain relationships of wood depend on the direction of the load relative to the grain and the type of load (tension, compression, or shear). The stress-strain relationships of wood in parallel tension, perpendicular tension, and shear are typically linear to brittle failure, while the stress-strain relationships of wood in parallel compression and perpendicular compression are typically nonlinear and ductile.
Another factor that affects the measured stress-strain relationships is moisture content. The stress-strain behavior of southern yellow pine in tension and compression is plotted in figure 3 as a function of moisture content. The data indicate a factor of up to three variations in strength with moisture content. The data also demonstrate brittle behavior in tension versus ductile behavior in compression. Saturation refers to the fiber saturation point, which is approximately 23 percent. The behavior in shear was not measured.
It is important to distinguish between the modes of failure because the effect of each mode on the ultimate strength of the wood posts may be quite different. For example, impacted wood posts have been observed to fail by parallel tensile and shear mechanisms. Thus, ultimate wood post failure occurs in the brittle modes (parallel to the grain), not the ductile modes. It is possible for perpendicular yielding to precede parallel failure, but not be catastrophic.
Measured stress-strain relationships of southern yellow pine depend on load direction (parallel or perpendicular), load type (tensile or compressive), and moisture content.
Temperature also affects the behavior of wood. This is demonstrated in figure 4 for wood posts impacted by bogie vehicles at 9.4 meters per second (m/s). There is a difference of a factor of 3 in measured response (force and velocity) between the frozen and unfrozen posts, which are made of southern yellow pine. The measured response of the Douglas fir post lies between that of the frozen and unfrozen southern yellow pine posts.
Wood exhibits progressive softening, as demonstrated by the splitting test data shown in figure 5 for southern yellow pine. In addition, wood exhibits modulus reduction and permanent plastic deformation, as demonstrated by the cyclic load curve shown in figure 6. Modulus reduction is indicated by the decrease in the elastic loading/unloading slopes as strain softening progresses. Permanent deformation is evident because the data unloads to zero stress at nonzero values of strain. The fracture area is the area under the load-displacement curve following peak stress. The data were obtained from splitting tests conducted by Stanzl-Tschegg, et al.(8) Although the data are for spruce wood, similar behavior is expected for pine and fir.
Temperature affects the dynamic behavior of wood posts impacted by bogies at 9.4 m/s.
Wood exhibits progressive softening. Source: Forest Products Laboratory.(9)
Wood exhibits modulus reduction and permanent deformation (splitting test data for spruce wood from Stanzi-Tschegg, et al.).
Source: Kluwer Academic Publishers, with the permission of Springer Science and Business Media.(8)
Wood is a variable material. The variability of the clear wood properties of southern yellow pine is given in figure 7 for tension parallel and compression perpendicular at 12 percent moisture content. The variability at other moisture contents is given in appendix A. Note that strength measurements vary by about a factor of 2 at each moisture content. In general, material properties vary as a function of position in a post, board, or test specimen. This is usually caused by natural variations in density; the presence of latewood and earlywood growth rings; and defects and growth characteristics, such as knots, checks, and shakes. Latewood is typically denser and stronger than earlywood. Knots, in particular, reduce the strength of wood. The reduction in strength depends on the knot size relative to the board size; the knot position (edge, center); and the wood parallel tensile strength, as shown in figure 8. Bogie impact tests indicate that the peak force in DS-65 posts is about 40 percent greater than that in grade 1 posts.(10)
Finally, wood exhibits an increase in strength with strain rate. This is demonstrated in figure 9 for various wood species.(11) The stress ratio increases with impact velocity and is most pronounced in the perpendicular direction. The stress ratio is the dynamic-to-static ratio measured in the Hopkinson bar tests. Rate effects are important when modeling vehicle collisions into wooden roadside structures.
Variability of southern yellow pine clear wood data at 12-percent moisture content depends on load direction and type.
Wood material properties vary with position. Board strength depends on position and size of knot.
Source: Society of Wood Science and Technology.(12)
Dynamic strength of wood increases with impact velocity in Hopkinson bar tests and is most pronounced in the perpendicular direction.
Source: Pergamon, Elsevier Science Ltd.(11)
1.2 OVERVIEW OF FORMULATION
The wood model consists of a number of formulations that are merged together to form a comprehensive model:
Each of these formulations is discussed separately. The flowchart in figure 10 shows how each formulation interacts with the others.
Each formulation requires specific input parameters, such as stiffness, strength, and fracture energy. The main source of the material properties listed in this section and used as default input parameters is the data measured by Forests Products Laboratory (FPL) for southern yellow pine as a function of moisture content.(13,14) FPL data are plotted in appendix A.
It is important to note that the FPL data are for clear wood (small specimens without defects such as knots), whereas real-world posts are graded wood (grades 3, 2, 1, or DS-65). Clear wood is stronger than graded wood. Nevertheless, the clear wood data are used as the basis for the default material properties. To account for strength reductions as a function of grade, reduction factors are applied to the clear wood strengths. Our reduction factor methodology is thoroughly discussed in section 1.12.
Organization of wood material model.