Fiber breakage criterion according to Puck

The fiber fracture criterion puck is used to calculate the failure of fiber reinforced polymer composites to fiber breakage . In contrast to simple fiber break criteria, it also takes into account the influence of stresses across the fiber.

Extension of the simple fiber break criterion

The simple fiber break criterion is based on the uniaxial comparison of the tension parallel to the fiber with the strength parallel to the fiber ; depending on whether a fiber parallel tensile or compressive stress is applied, the fiber is parallel to R train - and compressive strength used. According to this criterion, the component fails precisely when the tension parallel to the fiber reaches the strength parallel to the fiber: ${\displaystyle \sigma _{\|}}$ ${\displaystyle R_{\|}}$

${\displaystyle {\frac {\sigma _{\|}}{R_{\|}}}=1}$

The simple fiber break criterion is thus similar to the strength verification for metallic materials with the help of a comparison stress .

In the case of tensile stresses across the fiber, however, the tension parallel to the fiber increases due to the influence of the transverse contraction ; In contrast, pressure perpendicular to the fibers can lower the tension parallel to the fibers . If high tension parallel to the fiber and perpendicular to the fiber occur at the same time, the fiber breakage criterion according to Puck is applied. With this extended break criterion , the multiaxial stress state (parallel and perpendicular to the fibers) is transferred mechanically correctly to the simple fiber break criterion, in that the differently oriented stresses are first combined to form a resulting stress parallel to the fibers.

Mathematical formulation

The resulting, fiber-parallel tension is converted into the above. simple fiber break condition is used (and depending on whether it is positive or negative, the fiber tensile strength or fiber compressive strength is selected as before): ${\displaystyle \sigma _{\|}^{\rm {res}}}$ ${\displaystyle \sigma _{\|}^{\rm {res}}}$

${\displaystyle \sigma _{\|}^{\rm {res}}=\sigma _{1}-\left(\nu _{\perp \|}-{\frac {E_{\|}}{E_{\|,f}}}\cdot m_{\sigma }\cdot \nu _{\perp \|,f}\right)(\sigma _{2}+\sigma _{3})}$

With

• ${\displaystyle \sigma _{1}}$ : tension parallel to the fibers
• ${\displaystyle \sigma _{2},\sigma _{3}}$ : tension perpendicular to the fibers
• ${\displaystyle \nu _{\perp \|}}$ : large Poisson's ratio of UD layer
• ${\displaystyle \nu _{\perp \|,f}}$ : large Poisson's ratio of the fiber
• ${\displaystyle E_{\|}}$ : fiber-parallel module of the UD layer
• ${\displaystyle E_{\|,f}}$ : fiber-parallel module of the fiber
• ${\displaystyle m_{\sigma }}$ : Magnification factor (according to Puck : GFK 1.3 and CFK 1.1).

See also

• Failure criteria for fiber-reinforced plastics

literature

• A. Puck: Strength analysis of fiber-matrix laminates . Hanser, 1996. ISBN 3-446-18194-6
• H. Schürmann: Constructing with fiber-plastic composites . Springer Verlag, 2005. ISBN 3-540-40283-7

Web links

• Concept of a calculation process for components made of fiber composite materials (accessed on January 6, 2020)
• Investigation of numerical modeling methods for connections of sandwich structures in aircraft construction (accessed on January 6, 2020)
• Material-appropriate joining of fiber composite profiles (accessed on January 6, 2020)
• Automated construction of finite element models for connecting fiber composite components (accessed on January 6, 2020)
• Investigations into the load-bearing behavior of hybrid composite structures made of polymer concrete, fiber-reinforced plastics and wood (accessed on January 6, 2020)