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en:grundlagenhandbuch:faserbruchberechnung [2026/06/13 16:22] – deppe2en:grundlagenhandbuch:faserbruchberechnung [2026/09/04 13:17] (aktuell) – [Modeling] paal
Zeile 33: Zeile 33:
 For a description of this behavior the following differential equation is used: For a description of this behavior the following differential equation is used:
  
-$$\frac{dl}{dt} = c \cdot l^{\infty} ; \text{with} l = \frac{L - L_{\infty}}{L_0 - L_{\infty}} \tag{1}$$+$$\frac{dl}{dt} = c \cdot l^{\infty} ; \text{with } l = \frac{L - L_{\infty}}{L_0 - L_{\infty}} \tag{1}$$
  
 The origin of this equation refers to the initial glass fiber length $L_0$ with a dimensionless fiber length $l$, which describes the relation of the current glass fiber length $L$ to the initial fiber length $L_0$. The equation profile asymptotically approaches a process-limited fiber length $L_{\infty}$. The further parameters describe the speed $c$ and the sensitivity $α$ in terms of a fiber breakage. The origin of this equation refers to the initial glass fiber length $L_0$ with a dimensionless fiber length $l$, which describes the relation of the current glass fiber length $L$ to the initial fiber length $L_0$. The equation profile asymptotically approaches a process-limited fiber length $L_{\infty}$. The further parameters describe the speed $c$ and the sensitivity $α$ in terms of a fiber breakage.
Zeile 41: Zeile 41:
 For a solution of this differential equation and in particular for determining the process-limited fiber length $L_{\infty}$ the preliminary considerations about flow processes in twin-screw extruders are used. For a solution of this differential equation and in particular for determining the process-limited fiber length $L_{\infty}$ the preliminary considerations about flow processes in twin-screw extruders are used.
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_faserbruchberechnung_003.svg?nolink&300 |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_faserbruchberechnung_003.svg?nolink&500 |}}
  
 **Figure 3:** Shear flow stress on a fiber **Figure 3:** Shear flow stress on a fiber
Zeile 55: Zeile 55:
 Here $E$ is the fiber-Young's-modulus, $I$ the minimal moment of inertia of the fiber and $L$ the fiber length [[en:grundlagenhandbuch:faserbruchberechnung#references |[BG97]]]. Here $E$ is the fiber-Young's-modulus, $I$ the minimal moment of inertia of the fiber and $L$ the fiber length [[en:grundlagenhandbuch:faserbruchberechnung#references |[BG97]]].
  
-{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_faserbruchberechnung_004.svg?nolink&500 |}}+{{ :en:grundlagenhandbuch:en_sigma150_dlg_grundlagenhandbuch_faserbruchberechnung_004.svg?nolink&300 |}}
  
 **Figure 4:** Euler buckling **Figure 4:** Euler buckling