Numerical Analysis of Impact Loading of Adhesive Joints

Due to small repeatability of results of impact strength of adhesive joints, particularly those performed on di2erent test machines, the authors were inspired to conduct experimental and numerical research in this 4eld. ,e investigation used the Block Shear Test. ,e authors compared impact strength of samples which were loaded in a normative and nonnormative manner and also the dependence in impact strength with regard to the distance between the impactor’s edge and the surface of the bonded joint. ,e numerical calculations were carried out in the program Ansys, using the Explicit Dynamics module. ,e authors proposed a way of modelling the impactor of the pendulum hammer. It was found that a change in the direction of applying the load to the sample and rotating the loaded sample piece in relation to the edge of the impactor results in a signi4cant change in the Max Principal Stresses. Numerical investigations show that lower values of Max Principal Stresses occur in joints which are characterized by larger impact strength, determined experimentally. It was also noted that moving away the edge of the impactor from the surface of the adhesive joint increases normal stresses perpendicular to the surface of the joint.


Introduction
Adhesive connections are becoming increasingly used structural connections, in many cases replacing or supplementing traditional mechanical connections [1].While the subject of static strength of adhesive bonds is quite well known and discussed in literature [2], the issue of impact strength of adhesive joints has been the subject of a smaller number of experiments or theoretical deliberations.Among the research methods described in the available literature, it is possible to distinguish three most commonly used methods: (i) e Block Shear Test (BST) [3,4] (ii) e Impact Wedge Peel Test (IWPT) [5,6] (iii) e method of impact shear of lap samples loaded in tension [7][8][9][10] e problems occurring during the investigation of impact strength of adhesive joints are associated with large discrepancies of research ndings and their low repeatability on test machines manufactured by di erent producers [2,11,12].erefore, it is di cult to evaluate such results as well as using them in practice for the assessment of glued structure strength.
We made an attempt to carry out a numerical analysis of the Block Shear Test method (Figure 1).
We conducted an investigation of the Block Shear Test of such samples using di erent directions of the applying the load, and then we conducted a numerical analysis of both cases in order to nd relationships between impact strength of the examined samples and the distribution of stress values in the joints.We also checked experimentally the e ect of the distance between the impactor's edge and the bondline as well as a slight twisting of the hit sample surface against the edge of the impactor, upon impact strength and stresses in the joints.

e E ect of the Strike Direction upon Impact Loading of Block Samples.
e sample elements were made with steel S235.e bonded surfaces were exposed to abrasive blasting with copper slag.We obtained surface roughness of mean arithmetic deviation of the pro le from the mean line Ra 4.28 µm.After washing with petrol and drying, the elements of the samples were joined with Epidian 57/Z1 and hardened for 7 days at ambient temperature under the pressure of 40 kPa.e investigation was carried out on a special pendulum hammer whose maximum energy was equal to 15 J. e impactor struck the bonded plate at 0.8 mm over the bondline.e investigation was conducted for two directions of strikes (Figure 2).For each set of samples, we determined the mean value of impact strength as well as specifying a con dence interval by means of Student's t distribution for the con dence level of 1−α 0.95.ere was a signi cant di erence in impact strength depending upon the direction of the pendulum hammer's strike.e impact strength of identically bonded samples during normative testing was 8.5 ± 3.2 kJ/m 2 and 16.8 kJ/m 2 during nonnormative research.

Distance between the Edge of the Impactor and the Adhesive Joint.
In the tests, we used a nonnormative direction of applying the impact of energy equal to 15 J. e distance between the edge of the impactor and the joint was determined by means of a feeler gauge.In the examination of the subsequent series, by means of special spacers, we either decreased or increased the distance of the lower edge of the pendulum hammer from the adhesive joint by 0.2 mm.For the sake of safety of the test device, the smallest distance of conducting the test equalled 0.4 mm. e largest distance in the testing equalled 1.6 mm. e ndings of the experimental tests with marked con dence intervals are presented in Figure 3.
As a result of changes in the distance to the bondline, the measured impact strength also changed.e highest impact strength was characterized by adhesive joints, in which impact was applied the closest to the joint.Increasing the distance from the bondline resulted in lowering the registered impact strength of the joints.is phenomenon most possibly results from increasing the value of the applied moment, causing the tear-o of the front part of the upper part of the specimen.e results of the experimental studies were consistent with those presented by Adams and Harris [3].In the range of 0.4 to 0.8 mm distance from the bondline, the impact strength   2 Advances in Materials Science and Engineering changes to a slight extent.e fall in impact strength is particularly noticeable after exceeding the distance of 1.0 mm. e lowest impact strength was characterized in joints where impact loads were applied at a distance of 1.6 mm away from the adhesive joint; the drop in impact strength equalled more than 65% with regard to adhesive joints, which were impact loaded at a distance of 0.4-0.8mm from the joint.

3. e E ect of Load Application at a Slight Angle.
We examined joints in which the edges of the upper element were not parallel to the edge of the lower part of the sample (Figure 4).When putting the samples together, the upper element in each sample was intentionally rotated at an angle of 0.5−4 °± 0.5 °. e measurements of the obtained angles of element rotation were taken after curing the joints.e number of the bonded samples in each series varied (above 6 pieces), as it was impossible to precisely set the angles of the spacer while gluing.e values of the angles of rotation of the upper elements obtained in the selected series of the samples were as follows: 1.6, 2.4, 3.0, and 3.7 °.
In the investigation, we used a nonnormative strike direction of the hammer with energy equal to 15 J. e course of the selected tests was recorded by means of a high-speed camera in order to determine whether the impactor rotates or twists around its axis, while striking the edge of the sample.e analysis of the records led to the conclusion that even with the slightest obtained angles of geometry irregularities of the sample, the impactor does not revolve about its axis; if the sample is glued improperly, the load is applied to one (more protruding towards the impactor) vertical edge of the upper element.
e analysis of the video recording facilitated building an impact loading model for the sake of numerical investigations conducted in the next step.e ndings of the experimental tests are presented in Figure 5.
e analysis of the chart (Figure 5) con rms a crucial in uence of proper positioning of sample elements on the obtained research ndings.
e average impact strength of the control samples (bonded without rotation of the samples from each other) amounted to 17.85 ± 3.21 kJ/m 2 and the samples in which the upper element was rotated against the lower one by approximately 5.89 ± 0.68 kJ/m 2 .
e rotation of the upper element of the  Advances in Materials Science and Engineering sample against the lower element, even at a small angle, brings about a signi cant change in impact load conditions.e impact strength of samples, in which the elements are rotated, is over 65% lower with regard to the control samples.

Numerical Analyses
e calculations were carried out in the program Ansys, using the Explicit Dynamics module.We built a simple numerical model of the sample, which was divided into 8-node hexahedral nite elements (Figure 6), dedicated for dynamic computations (impact strength).In the modelling, we used the contact connection bonded-type Solid to Solid.
As we knew the mass of the pendulum hammer and its initial energy, it was possible to calculate the speed at which the impactor strikes the adhesive sample, that is, 2960 mm/s.In order to re ect the impactor's mass, we increased the density of the material to an extent that was declared for its manufacture so that it could be equal to the mass of the actual device.While declaring Young's modulus of the dropping tool as the one that corresponds to steel, it underwent excessive distortion, and therefore it obtained the properties of a rigid body.Eventually, the models of the tested samples were impact loaded with a dynamically rigid model (we used the rigid element) of the cuboid impactor with dimensions 5 × 25 × 3 mm, with the speed of 2960 mm/s and the density of 9.2 10 6 kg/m 3 , corresponding to the actual impact energy of the hammer used in the experiment (15 J). e calculations were carried out for two directions of the hammer and when the glued piece was slightly rotated towards the edge of the impactor.We compared the distributions of Max Principal Stresses in the joints for the same computational times, assuming that higher stress values should correspond to lower impact strength.Figures 7-9 present maps of distributions obtained in numerical calculations of the Max Principal Stresses calculations for the distance of 0.8 mm between the impactor's edge and the bondline.4 Advances in Materials Science and Engineering It was con rmed that lower impact strength which results from the load direction or twisting of the element which is torn o by impact loading corresponds to greater stress values; however, we did not nd quantitative correlation between impact strength and stresses.
In the further part of the numerical computations, the impactor was modelled as an element consisting of two parts-the piece striking directly into the sample was given steel properties; the other one had the modulus of elasticity higher, by one order of magnitude (2000 GPa), so as to ensure adequate sti ness of the striking element (Figure 10).
We analyzed the stress relationship in the joints, between the distance of the impactor's edge and the surface of the joint for the times corresponding to the maximum stress values (Figures 11 and 12).
e results of the analysis of the maximum stresses at the time of 2.4 × 10 −4 s were not in line with the results of the experimental research.
e calculations show that moving the edge of the impactor from the joint's surface results in an increase in normal stresses perpendicular to it (σ y ), which may be the cause of the decrease in impact strength of the tested connection.Due to the fact that stresses σ y cause the adhesive joint to tear o , adhesive strength may then exert a decisive in uence upon impact strength of the block connection in question while moving away the impactor's edge from the joint.
We also made an attempt to declare in the conducted dynamic calculations the model of damage related to the occurrence of Maximum Principal Stress in the adhesive (Max Tensile Stress 80 MPa and Max Shear Stress 80 MPa) (Figure 15).

Advances in Materials Science and Engineering
However, these ndings cannot be considered reliable, since numerical programs calculate reduced stresses in accordance with the von Mises hypothesis and destruction began at the site of maximum compressive stress.Adhesives, just like ceramic materials, though to a lesser extent, are characterized by higher compressive strength than tensile  Advances in Materials Science and Engineering strength.For this reason, the program regards it as critical stresses (destructive) occurring in the rear part of the joint, where compressive stresses are dominant (Figure 16).
We also examined how the time histories of normal principal stresses in the joints of dynamically impact-loaded block samples change if the glued elements are made of di erent materials and the adhesive is characterized by various sti ness (Figure 17).e conducted calculations proved that reducing the sti ness of both the joined elements and the adhesive itself leads to time extension, in which there are stresses in the joints as well as reductions of the value of Max Principal Stresses, which may cause increased impact strength.Advances in Materials Science and Engineering characterized by larger impact strength, determined experimentally.(iii) e drop in impact strength of block samples along with moving away the impactor's edge from the bondline is caused by a signi cant rise in normal stresses, perpendicular to its surface.

Conclusions
(iv) e ndings of impact strength tests performed on the very same test station are characterized with large discrepancies, which is caused by the dimensional tolerance of particular samples and requires their modi cation in order to eliminate the likelihood of their uneven load.(v) Impact strength of adhesive joints, which is determined experimentally, largely depends upon the sti ness of the research test rig.

Figure 4 :
Figure 4: Sample with the upper element rotated at an angle of approximately 3.7 °.

Figure 5 :
Figure 5: Impact strength of joints with a rotated spacer.

Figure 6 :
Figure 6: 3D model of the sample with a bonded cuboid element.

Figure 7 :Figure 8 :
Figure 7: Map of Max Principal Stress distribution in the joint for the computational time equal to 0.0001 s, under normative loading (Figure 2(a)).

Figure 9 :Figure 10 :
Figure 9: Map of Max Principal Stress distribution in the joint for the computational time equal to 0.0001 s, sample rotated against the impactor at angle of 3 °.

Figure 11 :Figure 12 :
Figure 11: Distribution of Max Principal Stresses in the joint of a block sample (distance from the impactor's edge to the bondline equals 0.8 mm).

− 5 Figure 13 :Figure 14
Figure 13: Distribution of Max Principal Stresses in the joint of the block sample when Max Principal Stresses reached tensile strength of the adhesive.

Figure 15 :Figure 16 :Figure 17
Figure 15: Changes in Max Principal Stress distributions in time, during dynamic impact loading of the block sample with declared adhesive tensile strength of 80 MPa.