Simulation study of a crampon – News

Composites make products light, yet strong. Designers are pushing the limits of what minimal material is needed to guarantee sufficient strength. Simulations help with this, but can be very computationally intensive for composites and therefore expensive. Reden, a specialist in product development and virtual testing, developed an effective method for predicting the failure behavior of composites and applied it to the design of a crampon.

Author: Hans van Eerden

 

Thermoplastic composites can contribute to sustainability because they are light, yet strong. As a result, less material is required for a product and, due to its low weight, it saves on fuel (and thus CO2 emissions) in applications in cars and planes, for example. Therefore, the EU stimulates the development of composite technology, as in recent years with the subsidy project PRODUCE. In it, Cato Composites from Rheden developed cost-effective production technology for sustainable thermoplastic composites. An important point of attention was the modeling of production processes and critical product properties, such as failure behavior of composites.

 

crampons

The design of a crampon for the German Burkhard Baumsteigtechnik served as a concrete case. The motive here was not so much sustainability as user comfort. An arborist uses a crampon when climbing up the tree along the trunk. The crampon is attached to the shoe and the lower leg and is provided with a ‘nail’ at the ankle, which is inserted into the tree trunk when climbing. In the usual embodiment, the shaft is made of the lightweight metal aluminum. With a view to wearing comfort for climbers, the goal was to achieve a further weight reduction of 50 percent for the shaft. This could be done by making the griddle out of composite. Such a crampon must of course be safe and meet the standards. For personal climbing equipment, ASTM F887-18: The crampon base must be capable of withstanding a vertical load of 3,300 N with the spike clamped and the shaft attached at the top.

 

ironCrampons from Burkhard Baumsteigtechnik (brand name Distel) made of aluminum (left) and composite.

 

Thermoplastic composites

Continuous fiber reinforced plastic composites consist of long fibers in a plastic matrix. The fibers are, for example, glass or carbon fibres, and two variants are used for the matrix, thermosetting and thermoplastic. For example, the blades of large wind turbines are made of thermosetting composites. However, production is labor-intensive and recycling is difficult. Thermoplastic composites do not have these disadvantages; their production is easy to automate and recycling is relatively easy. They are not suitable for use at high temperatures, because then – as the name indicates – they become soft. But they are already being used for car construction parts, and Cato Composites makes, among other things, helmets, suitcases, battery bags and leg protectors for skiers.

 

2.5D and 3D

Composite products are built up layer by layer from fiber mats that are anisotropic. They are strong in the fiber direction but weak in the transverse direction because fibers can be pulled apart; a well-known failure mode for composites. Therefore, the mats are placed on top of each other in alternating directions so that the resulting product is strong in several directions. This involves other failure modes: the meshes can detach (delamination) or move relative to each other (displacement). This makes it a challenge to describe and model the behavior of composites under load. This is exactly the challenge that Reden took on in this project, to substantiate the strength and rigidity of a product, in this case the frying iron.

 

Composites are often applied thin-walled in expanded shell products, and then a ‘2.5D’ description, in the plane of the shell, is sufficient for their mechanical properties and failure behaviour. However, the iron is a real 3D product: a long, curved shaft to which a belt and a nail are attached. Compared to its length, it is much thicker than a shell: with a thickness of 8-10 mm and a layer thickness of 0.1 to 0.2 mm, 50 or more layers must be stacked. Additional challenges for modeling and production are the curved shape and the necessary mounting holes, especially those for the nail. This is because large loads occur around the nail, which after all bears the climber’s weight and must absorb his ‘climbing forces’ (inserting and prying the nail).

 

Model description

A distinction can be made between three levels in the model description for products made from so-called unidirectional composites:

 

micro: the layer of fibers (typically 5-10 mi in diameter) that all lie in one orientation and with a certain volume fraction in a plastic matrix;

meso: the layers with their thickness and each their orientation;

macro: the fixation and loading of a product consisting of several layers.

 

With a homogenization technique, a material model can be made for a shell that is orthotropic (the properties in the plane are different than perpendicular to it). This model is processed into a scale element-based finite element model (hereafter referred to as the 2.5D model) with which the strain and stress due to an in-plane load can be calculated correctly. Loading perpendicular to the scale plane has no effect on the in-plane strain (σzz = 0). Damage due to overload is included in this model. Where it becomes ‘exciting’, for example due to bending or around holes, a volume element based finite element model (3D model) is needed.

 

Model optimization

Simulations were performed with the Abaqus software, known for its good composite simulation. For an efficient simulation, the trick is to use as much ‘cheap’ 2.5D description and as little ‘expensive’ 3D description as possible. This is possible by describing the product, the shaft in the case of crampons, mostly as a shell. To determine the transition from 2.5D to 3D description, Reden designed an iterative procedure. Based on an initial (2.5D) model, a load is applied and it is evaluated in which zones of the product the load and the load are too great for a 2.5D description to be sufficient. A 3D model is then used for the zones after which the load is increased. Again, the resulting load and stress are evaluated and the 3D model is expanded as needed. This is repeated until a stable, minimal 3D description is found.

 

The simulation challenge lies in the ‘point’ where the description of 2.5D changes to 3D. There is a 2.5D and a 3D finite element mesh connected to each other. The 2.5D scale has a thickness of zero, but the properties match the actual (3D) thickness. For a good connection, the 2.5D property (σzz = 0) must be imposed on the transition in the 3D part as a boundary condition.

 
clothes model

clothes model

Coupon test on test strips. Top: under stress, rejuvenation and eventually constriction occur Bottom: stress concentrations occur around a hole.

 

Model testing

To test the simulations against reality and to calibrate the model description, Reden performed coupon tests. Test parts were loaded to error. This is sufficient for normal, commercial tasks; after all, the intention is to stay away from this failure. The grant project allowed Reason to continue in the simulations and investigate a second and third drop after the occurrence of a first ‘drop’ in load and stress (due to damage such as delamination), to further refine the damage model.. The tests were carried out on simple strips to investigate the taper under load, not only in the transverse direction but also in the thickness direction. Until the failure occurred, the agreement between physical test and simulation was over 95 percent.

3D zones

The Crampon shaft model has two critical zones that require a 3D model description. The first is where the seam is attached with two bolts. The moment they are tightened can already ‘demolish’ the shaft. This must therefore be done with policy; For correct introduction of the prestressing forces, a cylindrical bushing is used, which has a conical outlet on one side. Coupon tests have also been performed with test strips with a hole in them, to study the occurrence of stress concentrations around the hole and to optimize the shaft design accordingly.

 

The second critical zone is where the shaft bends from the vertical upper part to the horizontal foot part. The production process – pressing layers stacked on top of each other in a mold – must ensure a good stress distribution in this curved part. The simulations were used to optimize the angle profile in the design.

 

clothes modelStress concentrations occur around the holes where the nail adheres to the shank, which can lead to damage to the fiber matrix.

 

Real comfort

The simulation study of the grid and its failure behavior has resulted in a design that meets the standard. Thanks to the comprehensive, precise simulations ‘to the point’, the iron does not need to be too heavy ‘just to be safe’. This gives the user true lightweight comfort. Burkhard Baumsteigtechnik now assembles the frying iron, with the composite handle produced by Cato Composites, in large numbers.

 

Ed

Reden in Hengelo (Ov) focuses on virtual, multi-physical testing of various products and processes for customers in markets such as food, medicine, automotive, (consumer) electronics, aerospace, production and high technology. The specialists in mechanics, thermodynamics, fluid dynamics and acoustics support the customer in his design problem with analysis, modeling and simulation & validation. In the end, Reden delivers a concept or feasibility study, a feasible design or a digital twin. Where possible, they translate their findings into knowledge rules that establish the relationship between design parameters and performance.

 

Reason performs tailored studies, where it tailors its tools, such as finite element methods, to the specific problem. An example is the simulation of a crampon described here. Reden has developed two software systems for automating design studies. Reves DSE is a tool for ‘design space exploration’ based on a system description. It works with input rules for knowledge, such as physical equations and relationships that describe connected subsystems. By varying the system parameters, Reves DSE then comes up with a variety of solutions to a design problem and can explore multiple use cases. Diamond offers ‘knowledge-based decision support’ for the design of processes and factories with modeling and optimization based on steady-state mass balance calculations.

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