Fracture Mechanics Parameters in Axial Compression Fracture of Thermoplastic Composite Cylinders


In today’s column, under the title of verification of fracture mechanics parameters in axial compression fracture of thermoplastic FRP cylinders, I would like to think about the analysis of FRP that involves fracture, with reference to a paper published in the Journal of the Japan Society of Materials Science.



A cylindrical GFRTP was used for evaluation

The papers referred to this time are as follows.

A. Koike etal, Effect of Interlayer Fracture Characteristics for Axial Crush of FRP Tube

The FRP to be evaluated is the so-called GFRTP, in which the matrix resin is PP (polypropylene) and the reinforcing fibers are randomly oriented glass fibers (presumed to be similar to a glass mat material).

It is called “a stampable sheet” in the paper. This name may come from JFE Chemical.

The fiber volume (Vf) is 40%, the longitudinal modulus is 5570 MPa, and the maximum tensile strength is 87.4 MPa.

Compared to GFRP, which is made by laminating general unsaturated polyester resin and glass mat by hand layup, both strength and elastic modulus are about half.


The reason for this is that the role of the GFRTP used in this evaluation is not only as a structural member, but also as a shock absorbing material that absorbs energy by breaking itself when an impact is applied. I think it comes from.



The evaluation shape is cylindrical, and the above GFRTP is laminated with 6 layers, and the tip is cut at an angle of 45° (chamfer-like shape).

Since the article describes it as a trigger, we believe that the purpose is to concentrate stress in order to advance the initial fracture from the tip when an impact is applied.



Modeling that introduces adhesive elements and considers nonlinear characteristics


The main purpose of this evaluation seems to be to verify what parameters should be set when GFRTP is destroyed.

Therefore, it is necessary to represent the fracture rather than a general linear analysis for rigid bodies.


In the model, adhesion elements are introduced between the layers, and the Traction Separation Loading Curve (TSLC) shown in Fig. 5 in the paper is introduced in order to evaluate the three stages of crack initiation, crack propagation, and final fracture.

In other words, we are trying to show by calculation that the behavior of each element changes continuously according to the external stress.

You can see that we are trying to capture rather complicated behavior compared to general analysis.


If the cylindrical shape is modeled as it is, the amount of calculations will be very large, so based on the principle that basically no breakage occurs in the circumferential direction, we extracted an arbitrary cross section of the cylinder and adopted a model that constrained the thickness direction. I am.

The model has 6 layers based on the actual number of layers, and each layer contains the adhesive elements described above.

Regarding the input physical properties of the material, enter the same elastic modulus as the initial value, and enter the yield strength (strength at which plastic deformation begins) as 100 MPa instead of the maximum tensile strength as the strength. The density is 1.6g/cm3 and Poisson’s ratio is 0.3.



Introduction of Energy Release Rate to Predict Fracture of Thermoplastic FRP


Something essential to express destruction. That is the energy release rate.

Instead of material mechanics, fracture mechanics will finally appear.


・Related columns

What is the energy release rate used in the first FRP toughness evaluation?


This time, we adopted GIc=3.0 J/m2 for the opening mode, Mode I, and GIIc=3.0 J/m2 for the shear mode, Mode II. Since there are no actual measured values, both modes are set to the same value, but it is worth knowing that if the matrix resin is thermoset, Mode II tends to display a larger value. Maybe not.

The paper states that in preliminary verification based on these parameter settings, it was possible to reproduce the same failure mode as in the actual test (Fig. 7).



External force is evaluated by a combination of normal stress and shear stress

The failure modes (setting the energy release rate) assumed this time are the opening mode, that is, the tension in the interlayer direction (thickness direction) and the shear mode, so multiple levels of external force are determined by combining these.

In the paper, the former is indicated as T, and the latter as S.

Details are provided in Table 3.



Fracture mode changes according to external force balance

Figure 9 shows the results of actually simulating fracture under multiple external force conditions.

As you can see, even if either S or T is constant, the failure mode changes when the other changes.

In particular, when T is constant and S is varied, the change is large, suggesting the fact that the failure mode changes greatly depending on the balance of external forces.


It has become clear that the fracture exhibits two tendencies: buckling-based mode in which interlaminar fracture progresses (described as progressive crushing), and the overall deformation of the side surface of the cylinder inward. I am.

For details, please see sections 5.1 and 5.2 in the paper.



Which GFRTP layer contributes the most to energy absorption?

The most interesting part of this paper is the main point.

I haven’t seen many examples that delve into the role of each layer in a simulation involving destruction.

We evaluate the energy absorption characteristics of each layer by performing a simulation in which a weight with an initial velocity collides with the cylindrical tip of the GFRTP.

As a conclusion, it is stated that the third layer from the inner surface among the six layers contributes the most to energy absorption.

The judgment was based on the fact that the energy absorption was greatest under conditions where the stress peaks overlapped in the layer concerned (Fig. 12).



Fracture simulation is essential to consider the application of FRP as a shock absorber


Nonlinear analysis is a more advanced task than the simulation (analysis) itself in that it is more difficult to prepare suitable material property data, as the results greatly depend on the accuracy of the input parameters.


On the other hand, there is no doubt that it is appropriate to consider FRP as a shock absorber as in this case.

The existence of an “interface” that exists due to the coexistence of incompatible materials, reinforcing fibers and matrix resin, complicates the behavior of fracture.

Therefore, it takes a long time to reach final destruction, and its special behavior allows it to easily absorb energy.


This may be one of the characteristics of FRP that is often overlooked.


On the other hand, in order to perform simulations that include fractures like this one, it is essential to have knowledge of not only material mechanics but also fracture mechanics, which may become increasingly difficult in this day and age where structural design skills are declining globally. there is.


I hope that this kind of steady effort to carefully verify FRP from a mechanical perspective will be revived, and that essential research and development will be carried out.

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