Method for simulating a fiber orientation in an injection-molded part made of a fiber-reinforced plastic, and design method for designing an injection-molded part made of a fiber-reinforced plastic

A method for simulating a fiber orientation in an injection-molded part made of a fiber-reinforced plastic, the method comprising:

• determining an orientation of the fibers in the injection-molded part to be manufactured that is present after the injection molding via a macroscopic simulation of the injection molding, and the macroscopic simulation of the injection molding taking place using macroscopic physical parameters of the fiber-reinforced plastic, wherein in the macroscopic simulation:
• determining a temporal development of a fiber orientation tensor via a combination of two macroscopic models, a first temporal development of the fiber orientation tensor being determined via a first macroscopic model of the two macroscopic models based on shear flows, and a second temporal development of the fiber orientation tensor being determined via a second macroscopic model of the two macroscopic models based on elongation flows;
• wherein first macroscopic physical parameters for the first macroscopic model and/or second macroscopic physical parameters for the second macroscopic model are ascertained via a micromechanical simulation;
• wherein the ascertainment of the first and/or second macroscopic physical parameters using the micromechanical simulation includes the following steps:
• a) forming a material cell including an ensemble of individual fibers that are embedded in a matrix material, fiber volume content and fiber length being predefined as input values,
• b) carrying out the micromechanical simulation in which the material cell is sheared at a predefined shear rate for a predefined period of time, or the material cell is stretched at a predefined elongation rate, at least the positions of the fibers of the ensemble being determined for each time increment of the simulation,
• interaction forces between two fibers in each case being determined during the micromechanical simulation, for at least a portion of the fiber-fiber interactions a pure interaction force being determined via a trained machine learning model, using input parameters of interaction angle, fiber aspect ratio, and distance between the fibers, and an interaction force being determined from a pure interaction force, using a linear relationship between viscosity of the matrix material and a relative velocity between the fibers.

A method for designing an injection-molded part made of a fiber-reinforced plastic, the method comprising:

• carrying out a simulation of fiber orientation including:
• determining an orientation of the fibers in the injection-molded part to be manufactured that is present after the injection molding via a macroscopic simulation of the injection molding, and the macroscopic simulation of the injection molding taking place using macroscopic physical parameters of the fiber-reinforced plastic, wherein in the macroscopic simulation:
• determining a temporal development of a fiber orientation tensor via a combination of two macroscopic models, a first temporal development of the fiber orientation tensor being determined via a first macroscopic model of the two macroscopic models based on shear flows, and a second temporal development of the fiber orientation tensor being determined via a second macroscopic model of the two macroscopic models based on elongation flows;
• and
• carrying out a weighting of an influence of the first macroscopic model and of the second macroscopic model on the temporal development of the fiber orientation tensor, determined in the simulation, based on a Manas-Zloczower number, limited to an upper value of 1 that corresponds to a pure elongation flow;
• determining a load-bearing capacity of the injection-molded part;
• and
• comparing the determined load-bearing capacity to a predefined load-bearing capacity.