Analysis of the Impact Resistance of Toecaps by the Finite Element Method: Preliminary Studies

A key property in the manufacture of toecaps for protective footwear is resistance to impacts, deformations, and cracking, as the resulting defects may lead to serious workplace accidents involving the lower extremities. The present paper proposes a new approach to qualitative verification of toecap design based on numerical simulations of impact tests. Computational experiments were conducted for toecaps made from different materials (AISI 10450, S235, S355 and A36 steels, as well as Lexan polycarbonate) and characterized by different geometries, which were recreated by 3D scanning. The impact resistance of the toecaps was analyzed using a numerical model simulating an experimental impact test. The results were used to determine the location of critical stresses and to plot equivalent stress maps for the studied toecaps. The finite element analysis of the impact tests was carried out with an explicit elastoplastic finite element code: ANSYS (Ansys, Inc., Canonsburg, PA, USA) with the Explicit Dynamics module of the Workbench solver. The presented analysis of the impact resistance of toecaps by the finite element method for impact simulation may be used to optimize the spatial geometry of toecaps and to verify the construction of toecaps and the material deformations that may occur. In addition, it could eliminate unsuitable materials that are likely to undergo dangerous deformations, and draw attention to the deformation caused by the impact of the toecaps used in footwear in the working environment.


Introduction
Toecaps are widely used elements of protective footwear that should be designed to meet the requirements of the EU's Regulation 2016/425 on personal protective equipment [1]. A defining property of toecaps is impact resistance [2], which is evaluated in accordance with the EN 22568 standard [3]. The toecaps applied in protective footwear are usually made of aluminum or high-strength steel [4]. Such materials are also widely used in the automotive industry for clutch disks, bumper reinforcements, and door impact beams to reduce the thickness of those elements, and thus decrease their weight, while preserving good mechanical properties [5][6][7].
The main advantages of metal toecaps include low production costs and good mechanical properties, such as high impact and crack resistance and low deformation, with the disadvantages of being heavy weight and having poor insulation parameters [8,9]. As a result, materials science strives to develop polymeric materials that would be characterized by strength properties and lower weight, compared to steel, while ensuring the appropriate functional properties of toecaps. Recent years have seen an increased application of non-metallic materials including composites incorporating polyester, polyamide, and epoxy resins with nanofillers (carbon, aramid, and glass fibers) [10][11][12][13]. Non-metallic materials are highly attractive due to their flexibility of design and additional features, such appropriate height to obtain an impact energy of either (200 ± 4) J or (100 ± 2) J, depending on the protection level claimed by the manufacturer. Impact-induced toecap deflection is assessed based on the smallest deflection point of the modeling clay cylinder, which reflects the clearance under the toecap upon impact. It should be noted that standard tests rely solely on modeling clay cylinder compression without assessing the stress distribution caused by the impact.
The impact test is described in standard BS 7971-4:2002 Protective clothing and equipment for use in violent situations and in training-Limb protectors-Requirements and test methods [28]. During the test, a 20 kg striker falls freely with gravitational acceleration (g = 9.8 m/s 2 ) from a height of 1075 mm. Initially, a body in free fall has a kinetic energy of E ko = 0 and gravitational potential energy E p = mgh, whereas at the end of the fall its kinetic energy increases to E k = mv 2 /2, with its potential energy being E pk = 0. In light of the law of conservation of mechanical energy, the initial and final sums of the kinetic and potential energies of a body are equal, which means that: Thus, the speed of the body at the time of impact on the surface can be obtained from the following equation: Since a body in free fall moves with constant gravitational acceleration (g), its final speed can be represented as: The preliminary studies of the analysis of the impact resistance of toecaps by the finite element method described in this paper can provide a qualitative verification of toecap design and help in optimizing toecap geometry and material composition; it can be also used to screen out materials that are unsuitable for protective toecaps in terms of deformations that are dangerous for the user in the working environment.

Materials and Methods
The preparation of the research material was initiated with 3D scanning of commercially available toecaps (metal and polymeric) and reconstructing the spatial geometry of the toecaps in a CAD file. The next step was to develop a computational model with boundary conditions reflecting the experimental impact test as described in the standard and including the mechanical properties of the selected materials in analysis. The Johnson-Cook model was applied and strength analysis and qualitative analysis of the selected geometries was evaluated.
The developed computational model simulates impact testing of steel and polycarbonate toecaps. Numerical strength modeling revealed critical stress areas in the studied toecap types.

Geometry Preparation Methodology
The study involved toecaps of two geometries (Table 1). Toecaps with geometry A were made from a thermoplastic polymer (polycarbonate), while type B toecaps were made from different grades of steel. The actual geometry of the toecaps was reconstructed by means of 3D scanning ( Figure 1). Toecap surface was mapped with a cloud of points used to create a triangular mesh, and finally a CAD model. Toecap surface was scanned using structural white LED light with an accuracy of 0.04 mm and a resolution of 73 points/mm 2 .

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by rear view

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five m were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of lected materials provided in Table 2. Simulations also took into account th

Johnson-Cook Model and Material Selection
Owing to incomplete material identification of the scanned toecaps, five materials were selected based on literature data, a polymer and four grades of steel: • Lexan-a polycarbonate; • AISI 10450-a quality heat-treatable non-alloy steel; • S235-a non-alloy structural steel; • S355-a high-strength low-alloy structural steel; • A36-a high-strength low-alloy steel.
Numerical calculations were based on the basic mechanical properties of the selected materials provided in Table 2. Simulations also took into account the Johnson-Cook parameters describing material hardening upon impact. The model is given by the multiplicative form of the constitutive equation, which is a function of strain, strain rate, and temperature: where: A = initial static yield stress for the reference parameters: ambient temperature T R and strain rate ε' 0 ; B = strain hardening constant; n = strain hardening exponent; m = thermal softening exponent; C = strain rate hardening coefficient; T = sample temperature; T m = melting point. The material constants A and B, as well as n, describe hardening under quasi-static conditions; the C parameter was determined by an interaction process from tension test data and it can be also found in Table 2. ε p is the accumulated plastic strain and ε 0 is the reference strain rate which, in this work, was taken as 1 s −1 . The effects of temperature were not included, as numerical analyses were performed for the standard temperature and heat values concerning to plastic strain are far from influence at these strain rates under consideration. The empirically determined Johnson-Cook constants for the studied materials are given in Table 3.

Analysis of the Impact Resistance of Toecaps by the Finite Element Method Finite Element Modeling
Mechanical strength analyses were conducted using numerical toecap models reflecting experimental impact attenuation tests pursuant to the standard BS 7971-4: 2002. Finite element modeling (FEM) was implemented in ANSYS Explicit Dynamics software. The computational model incorporated geometrical models, material properties, and boundary conditions. Analyses included the toecap geometry types A and B, which were reconstructed by 3D scanning of actual toecaps. The computational model was divided into four-node elements in a 3D space.
The numerical model was performed with three independent parts: the representative striker body, a bottom layer for the constrained support of the toecap, and the toecap model which performed the numerical analysis. The analysis model was developed on 3D solid elements. The toe cap model was discretized into tetrahedral structural solid elements with sizing mesh control. The other two solid parts were discretized into quadrangle-based prism elements (Figure 2).
Analyses included the toecap geometry types A and B, which were re 3D scanning of actual toecaps. The computational model was divided elements in a 3D space.
The numerical model was performed with three independent parts: tive striker body, a bottom layer for the constrained support of the toecap, model which performed the numerical analysis. The analysis model was 3D solid elements. The toe cap model was discretized into tetrahedral s elements with sizing mesh control. The other two solid parts were d quadrangle-based prism elements (Figure 2). The FEM boundary conditions included: the striker velocity vecto before impact Vk = 4480 mm/s; loading Q = 18.8 kg applied to the upper striker (to give an overall loading of 20 kg including the weight of the str and attachment with three blocked degrees of freedom (x, y, z) on the up the baseplate as shown in Figure 3.

Results and Analysis
Analysis of the impact resistance of toecaps by the finite element method showed that the maximum equivalent stress for one of the four steel toecap models exceeded the strength limits for the material (AISI steel), leading to toecap wall failure and fracturing. The obtained stress values were within acceptable limits for toecaps made from high-strength structural steel S355 and A36 (Table 4). Results for the two selected toecap models (geometry type A made from Lexan polycarbonate and type B from S235 steel) are presented in the form of Huber-von Mises equivalent stress and deformation maps. The deformation is described by the node with the maximum displacement in the Z direction, this represents how much the toecap is compressed.
In the analyzed models, the location of maximum stress and deformation largely depended on their shape. In polycarbonate toecaps type B, the greatest equivalent stress (80.3 MPa) was found in the middle of the upper wall near the area of impact (Figure 4), with the resulting deformation being 7.4 mm ( Figure 5). In turn, in steel toecaps type A the highest equivalent stress (approx. 500 MPa) occurred on the topmost edge of the upper wall and in the bottom segment near the baseplate (Figure 6). In toecaps made from S235 steel, upper wall deformation amounted to 5.34 mm (Figure 7).
Analysis of results also shows the importance of toecap material in safety footwear. Figures 8 and 9 show the node with the highest stress and deformation-value-over-time charts. Whereas all steel toecaps were characterized by the same geometry (type A), the strength curve for AISI 1045 steel differed unfavorably from the others, exhibiting a

Results and Analysis
Analysis of the impact resistance of toecaps by the finite element method showed that the maximum equivalent stress for one of the four steel toecap models exceeded the strength limits for the material (AISI steel), leading to toecap wall failure and fracturing. The obtained stress values were within acceptable limits for toecaps made from high-strength structural steel S355 and A36 (Table 4). Results for the two selected toecap models (geometry type A made from Lexan polycarbonate and type B from S235 steel) are presented in the form of Huber-von Mises equivalent stress and deformation maps. The deformation is described by the node with the maximum displacement in the Z direction, this represents how much the toecap is compressed.
In the analyzed models, the location of maximum stress and deformation largely depended on their shape. In polycarbonate toecaps type B, the greatest equivalent stress (80.3 MPa) was found in the middle of the upper wall near the area of impact (Figure 4), with the resulting deformation being 7.4 mm ( Figure 5). In turn, in steel toecaps type A the highest equivalent stress (approx. 500 MPa) occurred on the topmost edge of the upper wall and in the bottom segment near the baseplate ( Figure 6). In toecaps made from S235 steel, upper wall deformation amounted to 5.34 mm (Figure 7).
Analysis of results also shows the importance of toecap material in safety footwear. Figures 8 and 9 show the node with the highest stress and deformation-value-over-time charts. Whereas all steel toecaps were characterized by the same geometry (type A), the strength curve for AISI 1045 steel differed unfavorably from the others, exhibiting a highly irregular course. Indeed, toecap behavior under dynamic loads depends on the type of steel used. Ultimately, the stress-strain state of toecaps is affected by the material hardening phenomena caused by striker impact. In polycarbonate toecaps, there was a local stress concentration around the area of impact, whereas in steel toecaps the stress was distributed over a considerably larger area.
highly irregular course. Indeed, toecap behavior under dynamic loads depends on the type of steel used. Ultimately, the stress-strain state of toecaps is affected by the material hardening phenomena caused by striker impact. In polycarbonate toecaps, there was a local stress concentration around the area of impact, whereas in steel toecaps the stress was distributed over a considerably larger area.   highly irregular course. Indeed, toecap behavior under dynamic loads depends on the type of steel used. Ultimately, the stress-strain state of toecaps is affected by the material hardening phenomena caused by striker impact. In polycarbonate toecaps, there was a local stress concentration around the area of impact, whereas in steel toecaps the stress was distributed over a considerably larger area.

Discussion
The literature predominantly focuses on the static aspects of protective product testing, with the evaluated factors being correlations with absorption energy, mean crushing load, maximum peak load, stress distribution, and toecap deformation [5,12,34,35].

Discussion
The literature predominantly focuses on the static aspects of protective product testing, with the evaluated factors being correlations with absorption energy, mean crushing load, maximum peak load, stress distribution, and toecap deformation [5,12,34,35].
Some authors have explored cutting-edge technologies (mainly numerical modeling) in determining stress distribution, as well as toecap thickness and geometry optimization, with a view to improving resistance to mechanical factors [4,13,34,36]; these studies conducted computer simulations of the impact resistance of toecaps made from 1.2-1.8 mm thick martensitic steel sheets (Mart1200) using ANSYS software. Experimental tests were conducted using a Pegasil E-99 apparatus with a 25 kg striker and recorded with a highspeed camera at 5000 fps. The data were processed using TEMA Motion software. The numerical model consisted of the striker, toecap, and baseplate (support for the toecap). A modification of toecap geometry was found to improve its strength properties. Ribbed toecaps made of 1.2 mm thick steel revealed greater impact resistance as compared to non-ribbed toecaps made of steel sheets that were thicker by 0.3 mm.
An understanding of damage mechanisms at high stress and strain values is critical to the design of structures exposed to random impacts. Costa et al. [4] evaluated the impact resistance of steel toecaps made of two types of high-strength fully martensitic steels with a tensile strength of 1200 and 1400 MPa. The objective was to examine different toecap geometries with a view to maximizing the mechanical properties of toecaps while maintaining the ductility levels of steel needed for production processes. It was found that toecaps with considerably reduced thickness also revealed high impact energy absorption, despite significant deformation levels. In the author's studies the obtained stress values were within acceptable limits for toecaps made from high-strength structural steel S355 and A36.
Rodrigues et al. [37] evaluated a solid mechanics toolbox, built in the open-source computational library, OpenFOAM, to simulate compression and impact tests, which was used to assess commercially available plastic toecaps. The stresses developed during the impact tests are distinct from those in the compression tests, exhibiting a wave-like propagation form from the top to the bottom. In the present study, in polycarbonate toecaps, there was a local stress concentration around the area of impact. The greatest equivalent stress was found in the middle of the upper wall near the area of impact, with the resulting deformation being 7.4 mm ( Figure 5).
Lee et al. [13] analyzed the strength properties of fiber-reinforced plastic (FRP) toecaps, made from a glass fiber polyester composite, as compared to steel toecaps. ABAQUS software was used to conduct computer simulations of the dynamic and static forces acting on toecaps to optimize their thickness. The results of computer simulations were verified experimentally. In the case of steel toecaps, FEM revealed high tensile stress in their front part and compressive stress in the upper part, causing plastic deformation. In the case of composite toecaps, the highest compressive and tensile stress was found in the front part, which affected the type of impact-induced damage. The upper part of the toecaps revealed delamination and glass-fiber breakage. Preliminary analysis indicated the same values of toecap deformation at a wall thickness of 3.2 mm and 1.7 mm for composite and steel toecaps, respectively. The study also addressed the effect of reinforcement parameters (fiber type and distribution in the matrix) on the strength properties of the obtained composites. Toecaps containing layers of glass fibers with +45 • /−45 • orientation were characterized by the lowest static compression damage. In other orientations, the fibers tended to break. The application of a 0 • orientation led to the highest maximum deformation. In the other cases, deformation values were similar to, or lower than, those observed for the steel toecaps. Impact tests revealed that the highest stress and strain was lower in the composite toecaps than the steel ones. The higher absorbed energy was associated with breakage of the reinforcement and the matrix during the test. The composite toecaps were also characterized by much lower permanent strain. In terms of impact and compression resistance, the best results were found for the composite with glass fibers oriented at +45 • /−45 • and with glass mat layers on the external surface. Following damage to the upper part of the toecap, the load was transferred to a greater extent to its front part. In the present study, in polycarbonate toecaps (type B), the greatest equivalent stress (80.3 MPa) was found in the middle of the upper wall near the area of impact (Figure 4).
The available literature describes numerical simulations utilizing the finite element method to determine the highest stress concentrations and optimize material thickness and geometry, with a view to improving the impact resistance of toecaps.
The presented computational impact test analysis could be a useful support to the process of toecap design to increase user safety and comfort. Furthermore, it can be used to optimize the spatial geometry of toecaps and to verify the construction of toecaps and the material deformations, which pose a direct hazard to safety footwear users, that may occur.

Conclusions
The objective of the study was to perform analysis of the impact resistance of toecaps using the finite element method as a preliminary study for further, in-depth research into the analysis of the impact resistance of toecaps. The standard approach in toecap manufacturing is to produce a trial batch for experimental tests and verification of their impact resistance, which is both costly and time consuming. The numerical analysis of the toecap testing makes it possible to conduct preliminary evaluation without purchasing the necessary materials and launching production.
This study presented results on the response of safety toecap models, made of various steels and Lexan, investigated under quasi-static conditions at impact strain rates. The undertaken work contributes to better understanding the structural impact behavior of toe cap models.
The computational experiments were conducted on toecaps made from different materials (AISI 10450, S235, S355 and A36 steels, as well as Lexan polycarbonate) and characterized by different geometries. The results determined the location of critical stresses and plotted equivalent stress maps for the toecaps. In the analyzed toecap models, the location of maximum stress and strain largely depended on their shape and material. In polycarbonate toecaps the greatest equivalent stress was found in the middle of the upper wall near the area of impact. On the other hand, in steel toecaps, the highest equivalent stress occurred on the top-most edge of the upper wall and in the bottom segment near the baseplate.
Numerical simulation of mechanical strength behavior also provides opportunities for designing and optimizing toecaps made from composite materials, such as FRP. The application of material modeling at the stage of toecap design may accelerate the implementation of new materials with improved protective properties.

Conflicts of Interest:
The authors declare no conflict of interest.