A probabilistic virtual process chain to quantify process-induced uncertainties in Sheet Molding Compounds

Meyer, Nils; Gajek, Sebastian; Görthofer, Johannes; Hrymak, Andrew N.; Kärger, Luise; Henning, Frank; Schneider, Matti; Böhlke, Thomas

doi:10.1016/j.compositesb.2022.110380

Cited by 12 publications

(4 citation statements)

References 114 publications

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“…The large number of performed tests serves as an experimental data basis for a multiscale simulation approach. Similar to [9] for foams or [10] for sheet molding compound, the process-induced uncertainties of a short fiberreinforced polymer can be investigated. The mechanical properties of the polymer matrix and the fiber-matrix interface are necessary for microstructure simulations in a multiscale simulation approach.…”

Section: Discussion and Summarymentioning

confidence: 99%

Experimental Investigation of the Uncertainty of Disordered Fiber-Reinforced Injection-Molded Components

Rohrmüller,

Kneisel,

Hohe

et al. 2023

5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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Short fiber-reinforced composites manufactured by injection molding exhibit an alignment of the fibers superimposed by a manufacturing process induced scatter. As a result, the components possess a scatter in their mechanical properties due to the local scatter in fiber length, fiber orientation and fiber volume content. In this paper, we investigate the scatter of mechanical properties and fiber orientation of a glass fiber-reinforced phenolic resin with a fiber mass content of 37.5 wt% manufactured by a thermoset injection molding process [1]. Rectangular plates of 2 and 3 mm thickness and a size of 190 x 480 mm² were manufactured. The objective is to investigate the local variation of mechanical properties (Young's modulus, tensile strength and fracture strain) and fiber orientation and to evaluate the data statistically. Tensile tests are performed on miniature specimens of 36 mm length, 2 mm thickness and 2 mm width tested in 0° and 90° direction. The local mechanical properties are correlated with the local fiber orientation evaluated on in-plane micrographs taken on every specimen. On the 3 mm plates, tensile tests on specimens with shortened ISO dimensions are performed. The strain is evaluated globally and locally by digital image correlation (DIC). The investigated material shows fiber alignment in flow direction with the sprue positioned in the middle of the plates. The fiber alignment is superimposed by a large local process induced variation of the fiber orientation.

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Section: Discussion and Summarymentioning

confidence: 99%

Experimental Investigation of the Uncertainty of Disordered Fiber-Reinforced Injection-Molded Components

Rohrmüller,

Kneisel,

Hohe

et al. 2023

5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering

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show abstract

“…Fiber-orientation tensors [1] date back to the far-reaching works [2,3] and describe the relevant features of the fiber-orientation distribution of discontinuous fiber-reinforced composites. Within the virtual development and design process of such composites [1,[4][5][6], fiberorientation tensors appear in material modeling [7][8][9][10][11][12], microstructure generation [13][14][15][16][17][18][19], mold filling or flow simulations [20][21][22][23][24][25] and the experimental computer tomography analysis [26][27][28]. This wide field of application motivates a detailed understanding of the mathematical properties of fiber-orientation tensors.…”

Section: State Of the Artmentioning

confidence: 99%

On the Phase Space of Fourth-Order Fiber-Orientation Tensors

Bauer

Schneider

Böhlke

2023

J Elast

Self Cite

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Fiber-orientation tensors describe the relevant features of the fiber-orientation distribution compactly and are thus ubiquitous in injection-molding simulations and subsequent mechanical analyses. In engineering applications to date, the second-order fiber-orientation tensor is the basic quantity of interest, and the fourth-order fiber-orientation tensor is obtained via a closure approximation. Unfortunately, such a description limits the predictive capabilities of the modeling process significantly, because the wealth of possible fourth-order fiber-orientation tensors is not exploited by such closures, and the restriction to second-order fiber-orientation tensors implies artifacts. Closures based on the second-order fiber-orientation tensor face a fundamental problem – which fourth-order fiber-orientation tensors can be realized? In the literature, only necessary conditions for a fiber-orientation tensor to be connected to a fiber-orientation distribution are found. In this article, we show that the typically considered necessary conditions, positive semidefiniteness and a trace condition, are also sufficient for being a fourth-order fiber-orientation tensor in the physically relevant case of two and three spatial dimensions. Moreover, we show that these conditions are not sufficient in higher dimensions. The argument is based on convex duality and a celebrated theorem of D. Hilbert (1888) on the decomposability of positive and homogeneous polynomials of degree four. The result has numerous implications for modeling the flow and the resulting microstructures of fiber-reinforced composites, in particular for the effective elastic constants of such materials. Based on our findings, we show how to connect optimization problems on fourth-order fiber-orientation tensors to semi-definite programming. The proposed formulation permits to encode symmetries of the fiber-orientation tensor naturally. As an application, we look at the differences between orthotropic and general, i.e., triclinic, fiber-orientation tensors of fourth order in two and three spatial dimensions, revealing the severe limitations inherent to orthotropic closure approximations.

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“…Fiber-orientation tensors [1] date back to the far-reaching works [2,3] and describe the relevant features of the fiber-orientation distribution of discontinuous fiber-reinforced composites. Within the virtual development and design process of such composites [1,[4][5][6], fiber-orientation tensors appear in material modeling [7][8][9][10][11][12], microstructure generation [13][14][15][16][17][18][19], mold filling or flow simulations [20][21][22][23][24][25] and the experimental computer tomography analysis [26][27][28]. This wide field of application motivates a detailed understanding of the mathematical properties of fiber-orientation tensors.…”

Section: State Of the Artmentioning

confidence: 99%

On the phase space of fourth-order fiber-orientation tensors

Bauer¹,

Schneider²,

Böhlke³

2022

Preprint

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Fiber-orientation tensors describe the relevant features of the fiber-orientation distribution compactly and are thus ubiquitous in injection-molding simulations and subsequent mechanical analyses. In engineering applications to date, the second-order fiber-orientation tensor is the basic quantity of interest, and the fourth-order fiber-orientation tensor is obtained via a closure approximation. Unfortunately, such a description limits the predictive capabilities of the modeling process significantly, because the wealth of possible fourth-order fiber-orientation tensors is not exploited by such closures, and the restriction to second-order fiber-orientation tensors implies artifacts. Closures based on the second-order fiber-orientation tensor face a fundamental problem -which fourth-order fiberorientation tensors can be realized? In the literature, only necessary conditions for a fiber-orientation tensor to be connected to a fiber-orientation distribution are found. In this article, we show that the typically considered necessary conditions, positive semidefiniteness and a trace condition, are also sufficient for being a fourth-order fiber-orientation tensor in the physically relevant case of two and three spatial dimensions. Moreover, we show that these conditions are not sufficient in higher dimensions. The argument is based on convex duality and a celebrated theorem of D. Hilbert (1888) on the decomposability of positive and homogeneous polynomials of degree four. The result has numerous implications for modeling the flow and the resulting microstructures of fiber-reinforced composites, in particular for the effective elastic constants of such materials.

show abstract

A probabilistic virtual process chain to quantify process-induced uncertainties in Sheet Molding Compounds

Cited by 12 publications

References 114 publications

Experimental Investigation of the Uncertainty of Disordered Fiber-Reinforced Injection-Molded Components

Experimental Investigation of the Uncertainty of Disordered Fiber-Reinforced Injection-Molded Components

On the Phase Space of Fourth-Order Fiber-Orientation Tensors

On the phase space of fourth-order fiber-orientation tensors

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