MT06.11 Board level drop testing of PCB s

Transcription

1 MT06.11 Board level drop testing of PCB s John Kop, Gerben van den Oord, Dominic Swagemakers, Dennis van den Berg Coach: P. Schreurs, H. de Vries April 20, 2006

2 Contents Preface 3 1 Introduction JEDEC standards Test board Test procedure Failure results Experiments and calculations in this field Philips Applied Technologies STMicroelectronics The Model Structure and sizes Modeling Materials Rayleigh damping Theory Experiment Results Simulation Validation 23 4 Model possibilities 35 5 Conclusion and Recommendations 39 Bibliography 39 2

3 Preface In recent years, there has been an exploding increase in the amount of portable consumer electronics. The demand for portable music players, mobile phones or handheld computers has led to a change in requirements concerning the electronic hardware. Classically, electronic devices were stationary and the main reason for failure of printed circuit boards (PCB) was directly related to the temperature history. Successive warming during usage, and cooling down in idle periods makes the different components of the circuit board expand and contract at different rates and different amounts, thus creating stresses. Repeating these cycles during the lifespan of the product then causes fatigue-like failure. However, in the case of portable devices, mechanical loading can play an important role in failure of the electronics. A mobile phone can be dropped creating an impact load, or the integration of keypads on printed circuit boards can create loads under normal use. The behavior of circuit boards under mechanical loading isn t as well understood as the thermal behavior. Therefore a lot of experiments are needed in order to predict lifespan under different circumstances. Because of the sheer number of different printed circuit boards and different loading circumstances, these experiments can not be carried out for every device on the market and standard tests have been developed to gain insight in the problem. One of the companies performing these experiments is Philips Applied Technologies, which has asked the Eindhoven University of Technology to take a different look towards the problem. The university lacks the equipment to do these experiments itself, so it was obvious to look at the problem from a computational point of view: it would be a lot cheaper and faster if these kinds of test could be simulated in a finite element environment. The goal of this project therefore was to investigate if these computations are feasible and reliable enough to predict failure. To do this, first a simple model of a printed circuit board was made. This model does not contain the actual layered structure of the PCB and its internal copper connections, nor does it contain the electrical connections between the board itself and the chips mounted on it. Although failure of these connections largely determines the failure of the device as a whole, first the general behavior of the whole structure has to be simulated correctly. On the basis of this large scale model a small scale model could then be created containing one ore more connections. In this report, first the standards concerning research in this field are introduced along with two examples of such studies. In the second chapter a model is created to simulate board level tests. In the last chapter the model is validated with measurements from earlier studies. 3

4 Chapter 1 Introduction 1.1 JEDEC standards Standard tests have been developed to study the effect of dropping a printed circuit board (PCB) from some height to the ground. Standards provided by the JEDEC solid state technology association (JESD22-B111 [2], B104B [3] and B110 [4]) provide a description of the test methodology as well as the PCB itself, in order to simulate the failure modes that occur in actual product testing in a reproducible way Test board First of all, the JEDEC standards describe the test board in great detail. Not only basic measurements as shown in figure 1.1 are given, but also the layered structure that exists in a PCB (table 1.1) and properties of the used materials (table 1.2). In the basic measurements, the component size is taken to be 15 mm x 15 mm, which is roughly the largest component size used on PCB s for portable devices. Normally 15 components are mounted, but other numbers of components can also be used, as long as they are all the same. Furthermore, the type of component can be chosen freely, but nowadays ball grid arrays (BGA) are most common. On this kind of component, the connection between the component and the PCB are made on the bottom of the component with small balls of solder (figure 1.2). To be able to tell if a connection fails during drop testing, all components must be daisy chained so a failed connection can be measured as an increase in electrical resistance (greater than 1000 ohms for a minimum of 1 microsecond). This has to be measured during the actual test itself (in-situ), because cracks that appear in the material may be closed again when the PCB returns to its original shape Test procedure The test procedure is fully described as well. The test board has to be mounted on a rigid base plate using four screws with components facing downward to ensure maximum deflection. This connection is prescribed in great detail, to ensure reproducibility. The 4

5 1.1 JEDEC standards 5 Figure 1.1: Test board base plate in turn is fixed on a drop table so that there is no relative movement between the two. The drop table then is dropped from a predetermined height along two guide rails until it hits the base of the structure. To prevent bouncing, and therefore loading the PCB multiple times, a braking mechanism of choice must be used to stop the drop table after its first impact. The nature of the impact is determined by acceleration of the base plate which is measured by an accelerometer in the center of the plate or close to the PCB supports. The impact itself for the case of board level drops must meet certain requirements: the acceleration of the base plate must reach m/s 2 during a 0.5 millisecond long half sine pulse as defined in [4]. To generate an impact of this form, both drop height and strike surface properties can be changed. Further more, during the pre-testing phase, an accelerometer and strain gages can be attached to the PCB in order to characterize the response and to measure strain rates if components are used for which no data exists. For actual testing, the only things mounted to the PCB are the wires needed to perform measurements of electrical resistance of the daisy chains. To influence dynamical properties of the PCB as little as possible, these wires are soldered on the test board and no connector is used. Finally, the number of drops per board, and the number of boards per test are also specified for different conditions Failure results Measurements during drop testing can be made in two ways: either using an event detector, which only detects events such as stated above: an electrical resistance of 1000 ohms or greater for a minimum of 1 microsecond; or using high speed data acquisition to measure the actual resistance over time. 5

6 1.2 Experiments and calculations in this field 6 Board Layer Thickness Copper Coverage (%) Material (microns) Solder Mask 20 LPI Layer 1 35 Pads + Traces Copper Dielectric RCC Layer % including daisy chain links Copper Dielectric FR4 Layer % Copper Dielectric FR4 Layer % Copper Dielectric FR4 Layer % Copper Dielectric FR4 Layer % Copper Dielectric FR4 Layer % Copper Dielectric RCC Layer 8 35 Pads + Traces + Daisy chain links Copper Solder Mask 20 LPI Suggested RCC Material: Polyclad PCL-CF /35/35 Suggested FR4 Material: NELCO N or equivalent Table 1.1: Test board stack-up and material used In the first case, a failure is determined to have taken place at the first event, which also has to occur during at least 3 out of 5 subsequent drops of the test board. When using high speed data acquisition, failure is determined as the first indication of a resistance value of 100 ohms or 20% increase in resistance if the initial resistance is greater than 85 ohms, and again, this also has to take place during 3 out of 5 subsequent drops. Also, visible separation of component and PCB is considered as failure. By describing almost everything in full detail, the statistical data generated from these experiments are comparable to other experiments in the same field. In this way, different solders or other components can be studied. 1.2 Experiments and calculations in this field Many companies are involved in the design and fabrication of portable electronic devices and therefore feel the need to understand the response of dropping PCB s. Two of those companies will be discussed here. First of all Philips [5], being the initiator of this project, who performs drop tests according to the JEDEC standard. The second, STMicroelectronics [1], because they not only have done experimental drop tests, but also made a numerical model for simulating them, just as is the purpose of this project. 6

7 1.2 Experiments and calculations in this field 7 Property Unit FR4 RCC Tensile Strength MPa >100 >50 Tensile Modulus GPa 20±2 2±1 Tensile Elongation % >3 >3 In-plane CTE ppm/ o C 15± (below Tg) Tg o C >130 >130 Cu Peel kgf/cm >1 >1 Table 1.2: Properties of materials in the PCB Figure 1.2: Ball grid array (picture from Philips Applied Technologies Philips performs drop tests at Thales according to the JEDEC standard in order to study the effect of lead free solder opposed to the normal lead-tin solder. This is because lead holding solder will be prohibited for electronics in the near future. In their studies Philips focusses on both statistical data of numerous solders and failure modes. Statistical failure data of five different ball and interface compositions, is shown in figure 1.3. In this figure the total percentage of failed connections on a PCB is plotted against the number of consecutive drops. For failure mode analysis the PCB is covered in synthetic resin and grinded down to make a cross section of the failed area. Most often it seems that failure does not occur in the solder itself but in the PCB (substrate and copper connections) or in the interface in between the PCB and solder. Failure in the substrate can be seen in figures 1.4, failure in the copper connection can be seen in 1.5 and 1.6. Failure in the interface is shown in figures 1.7 and

8 1.2 Experiments and calculations in this field 8 Figure 1.3: Statistical drop test data Figure 1.4: Fracture in PCB STMicroelectronics As is the case for this project, STMicroelectronics, in cooperation with the National University of Singapore and the Nanyang Technological University, studied the behavior of PCB s when dropped to the ground. For this, they have done actual drop tests, while measuring acceleration near a fixed point on the PCB (near one of the screws), acceleration at the center of the PCB, strains in longitudinal and latitudinal directions of the PCB and the resistance along the electrical circuits of the PCB. The accelerometer near one of the screws is used to determine the input acceleration given to the PCB. (When performing experiments according to the JEDEC standard, this accelerometer is placed at the base plate). To observe the actual dropping, and to determine maximum deflections, a high speed camera was used (6000 frames/s). With this set-up, good correlation is found between output acceleration and strains at the PCB center. As could be expected, the PCB behaves much like a plate clamped at two 8

9 1.2 Experiments and calculations in this field 9 Figure 1.5: Fracture through first Cu6Sn5 IMC layer then metal line at the substrate side Figure 1.6: Details of figure 1.5 Figure 1.7: Fracture through Cu6Sn5 IMC layer at the substrate side. Left corner, no electrical failure found. Figure 1.8: Details of figure 1.7 sides; when acceleration is at a maximum, the PCB is at maximum deflection and also strains are at maximum (figure 1.9). Over a longer time, response shows cyclic bending, figure Further more, strains and resistances over the circuits also correlate. When the strain at non-component side (measured) is at a minimum (compression), the strain at the component side would be at a maximum (tension). This causes opening and closing of cracks in the solder joints, which result in an increase or decrease in resistance, respectively. This is shown in figure Just like in this project, STMicroelectronics set out to make a finite element model for this problem. They state that there are three levels of modeling this case; first, a model that gives a good representation of the PCB s dynamical response, second, a model that gives a qualitative trend of stresses and strains in the solder joints and third, a model that can predict impact life. Because strains and stresses in the solder joints can not be measured during testing, and impact life prediction needs very sophisticated material models, second and third level models are difficult to make and verify. However, a first level model can still be useful when making use of the close relationship between the PCB s dynamic behavior 9

10 1.2 Experiments and calculations in this field 10 (from a level 1 model) and solder joint reliability. Unfortunately, their paper doesn t tell much about the finite element model itself (build up, element type, element size, etc). However, it does show an easy way to deal with the experimental set up. When simulating the drop experiments using the drop height as input parameter, friction in the guides, nature of the strike surface and the behavior of the drop table has to be taken into account. This can take up a lot of calculation time which does not generate direct results. Fortunately, the final input into the PCB itself can be described by the acceleration of the four screws alone. This is a quantity measured during the actual experiments, and can therefore be used directly as input for the numerical model. In this way, the model only consists of the PCB (and components) itself, and all effects from friction etcetera are contained in the input acceleration (figure 1.12) on the four screw points. Using their model, the researchers were able to reproduce the experimental data in good detail for the strain in longitudinal direction and acceleration at the PCB center, as shown in figures 1.13 and In the next chapter, in the same way a model will be made for a PCB complying to the JEDEC standard as used by Philips [5]. Figure 1.9: Dynamic responses of the PCB Figure 1.10: Cyclic bending of PCB after drop impact Figure 1.11: Dynamic strain and resistance response showing crack opening Figure 1.12: Input acceleration curve 10

11 1.2 Experiments and calculations in this field 11 Figure 1.13: Strain in longitudinal direction Figure 1.14: Output acceleration at PCB center 11

12 Chapter 2 The Model Much information about impacts of PCB s comes from experimental investigations and little effort is put into simulation. In this project a beginning is made with the simulation of impact tests. MSC Marc/Mentat is used to model and simulate a PCB falling and crashing, for example a mobile telephone falling on the ground. In this chapter the model and simulation will be described. The simulation of impact is based on solving the following equation: M ẍ + C ẋ + Kx = f (t) (2.1) M is the mass matrix, C is the damping matrix, K is stiffness matrix and f are the forces acting on the system. From the output acceleration shown in figure 1.14 it can be concluded that the influence of damping must be taken into account. To solve this equation several boundary conditions are required, this will be discussed later in this paper. Using the Marc/Mentat software for the dynamic simulation the only possibility to include damping is introducing nodal damping or Rayleigh damping coefficients. Rayleigh damping is used to implement damping in the model. In this chapter the realization of the numerical model and theory of Rayleigh damping will be explained. 2.1 Structure and sizes One of the goals of this project is to simulate the impact of a PCB with a FE model and to compare the numerical results with the experimental observations. A detailed model of PCB with microchips and other features is very complicated so only the most important features are modeled. In figure 2.1 the model is shown. The PCB is modeled as a plane plate with uniform thickness subdivided in a mesh of about 26 x 9 shell elements. At the four corners, holes are left out, which represent the location of the fixations. On top of the PCB 15 parts of solder are placed and on it some material making up a microchip. Normally the solder layer consist of a number of solder bumps, but due to the difficulty in modeling it is simplified to a layer. Later details about the model will be described. The dimensions of the model are exactly the same as those of the test PCB s used in the Philips impact experiments according to the JEDEC standards. In figure 2.2 the model is shown again with the dimensions indicated. 12

13 2.2 Modeling 13 Two other PCB s are modeled, which are not used in the impact experiments but were used to determine the dynamic properties of the PCB s. These other two PCB s have the same size as the first one. One contains only one microchip in the middle of the plate and the other doesn t contain any microchips at all. Both models are shown in figure 2.3. Figure 2.1: Schematic view of the model made in MSC Marc/Mentat 2.2 Modeling The PCB is modeled as a shell because the thickness is very small compared to the width and length. The solder layers and the packages are also very thin compared to their width and length so they are modeled as a shell too. The microchip and solder layer are modeled as one shell, using the composite material model option to make it behave as two different layers. Both shells, the FR4 plate and the shell for the solder and microchip, have to be connected to each other. To model the PCB realistically the subdividing in elements is done such that the element nodes of the FR4 shell and the shells for solder and packages, are exactly above each other, as seen in figure 2.4. The position of the composite shell is at half the thickness of the FR4-plate plus half the thickness of the composite, containing the solder layer and the microchip. This is done because a shell is modeled as a plane with thickness as a parameter stored in the geometric properties. The modeled plane is exactly in the middle of the thickness. Now it is possible to connect these nodes, that are above each other, with nodal ties. The nodes that have to be connected are tied together in 6 degrees of freedom. For an example, see figure 2.5. Shell element 75 is used for the model, which contains four nodal points, with 6 degrees of freedom being displacements in and rotations about the three global coordinate axes. 2.3 Materials To connect all microchips and other electronic components to each other and to the outside world, a lot of copper lines are integrated in the PCB at different layers over the thickness. 13

14 2.3 Materials 14 Figure 2.2: Schematic view of the PCB with the sizes These copper lines are not modeled, the PCB is modeled as a shell consisting of only one material namely FR4. FR4 is a fiberglass reinforced epoxy. The fibres are oriented orthonomally in the length and width directions which are indicated as 1 and 2 in table 2.1, which lists the used material properties of FR4 [6]. Because this is only a simplification of an impact test, many properties like temperature influence are not necessary. On the PCB small layers of solder material are modeled. The material used for this solder is Sn63Pb37. The used properties of this isotropic material are shown in table 2.2. The packages are modeled as shells and placed on the solder layers. The packages are simplified a lot and are modeled as a polymer whose properties are also shown in table 2.2. To make the modeling more easy a composite material is used. A composite material consists of 2 or more different materials ordered in layers. The composite used consists of a very thin layer of solder material with a layer of the package polymer on top. For impact simulation damping has a big influence. In the next paragraph Rayleigh damping parameters are used for describing the damping of the whole system. 14

15 2.4 Rayleigh damping 15 Figure 2.3: Two other PCB s that are modeled Figure 2.4: Element subdividing 2.4 Rayleigh damping Theory In Marc/Mentat damping can be introduced as modal damping or Rayleigh damping. In this paper Rayleigh damping is used because it results in an averaged form of modal damping and it is difficult to match modal values from real experiments with modes found in simulation. The following derivation concerning Rayleigh damping is based on a reader by de Kraker [7]. Both Rayleigh and modal damping assume that the solution of equations of motion can be seen as a linear combination of different modes. These modes can be found by solving the eigenvalue problem of the free undamped system the eigenvalue problem then reads Mẍ (t) + Kẋ (t) = 0 [K ω 2 M] = 0 (2.2) (2.3) 15

16 2.4 Rayleigh damping 16 Figure 2.5: Nodal ties between both shells This gives n different squared eigenfrequencies ω 2 r and n eigenvectors u r. With this the linear combination of modes of each x (t) can be written as: x (t) = η 1 (t)u 1 + η 2 (t)u η n (t)u n (2.4) n x (t) = Uη r (t) = Uη(t) (2.5) r=1 In which η r is the modal participation factor for the corresponding mode u r. U is called the modal matrix. This transformation is linear, so that for the derivatives also hold ẋ = U η(t), etc. This theorem is called modal expansion. This transformation can now be applied to the relevant equations of motion for this problem, equation 2.1 (with f (t) = 0 ), resulting in MU η(t) + CU η(t) + KUη(t) = 0 (2.6) When this expression is premultiplied with U T this gives U T MU η(t) + U T CU η(t) + U T KUη(t) = 0 (2.7) In this, U T MU forms a diagonal matrix with modal mass fractions (m r ) and U T KU forms a diagonal matrix with modal stiffnesses (k r ). These modal stiffnesses can be written as m r ω 2 r. Now, in general, the combination U T CU will not be diagonal and this system of equations therefore will not be uncoupled and the system can not be solved easily. However, when damping matrix C is chosen to be a linear combination of the mass matrix M and stiffness matrix K (proportional damping) the combination U T CU will indeed be diagonal and the system equations will be uncoupled. In the case of Rayleigh damping: U T CU = α m r + β k r (2.8) 16

17 2.4 Rayleigh damping 17 Young s modulus (Pa) E e10 E e10 E e9 Poisson s ratio (-) ν ν ν Shear Modulus (Pa) G e10 G e10 G 13 7e8 Density(kg/m 3 ) 1500 Table 2.1: Material properties of FR4 Young s modulus (Pa) Poisson s ratio (-) Density (kg/m 3 ) SnPb e Package 2e Table 2.2: material properties of SnPb (solder) and package but also, from dynamics: = α m r + β m r ω 2 r (2.9) = m r (α + β ω 2 r ) (2.10) = d r (2.11) d r = 2ξ r ω r m r (2.12) In these equations α is the mass matrix multiplier, β is the stiffness matrix multiplier and ξ is the dimensionless modal damping factor which is normally used in dynamical analysis. To determine the Rayleigh parameters it is sufficient to know the undamped eigenfrequencies and corresponding dimensionless modal damping factors. However, in the case of proportional damping, undamped eigenfrequencies are equal to damped eigenfrequencies. So if proportional damping is assumed for the PCB a dynamical experiment can be carried out to determine damped eigenfrequencies and corresponding dimensionless modal damping factors. This experiment is described in the next section. Equating 2.10 with the right hand side of 2.12 and rearranging leads to: ξ r = α + βω r 2ω r 2 (2.13) From equation (2.13) it can be observed that the Rayleigh damping ratio is proportional to the natural frequencies of the system. One can also see that the mass matrix parameter α in particular creates damping for the low-frequency modes whereas the stiffness parameter β generates damping for the high-frequency modes as is indicated in fig

18 2.4 Rayleigh damping ξ [ ] β=0.1, α=0.1 β=0.1, α=0.0 β=0.0, α= Eigenfrequency ω [rad/s] Figure 2.6: Dimensionless modal damping factor When a natural frequency (ω r ) and its corresponding dimensionless modal damping factor (ξ r ) are known equation 2.13 is an equation with two unknowns (α and β). However α and β are supposed to be the same for every set of ω r and ξ r so when taking data from two eigenfrequencies, this gives two equations for two unknowns. Solving for β gives: β = 2ξ pω p 2ξ q ω q ω 2 p ω 2 q (2.14) For structures having many degrees of freedom only the first few modes, contribute to the significant dynamic behavior. For most engineering structures the number of significant modes is between 3 at the minimum and about 25 at the maximum. By back-substituting β in the expression the value of α can be obtained. 2ξ r ω r = α + βω 2 r (2.15) Experiment Doing structural frequency response testing, also known as modal analysis, it is possible to determine the natural frequencies and corresponding damping ratios of a structure. Response is measured using an accelerometer placed at a certain point of the structure under test (see figure 2.7 [8]). The placement of the accelerometer is of great importance. When it is placed in a point where the response of a certain mode is always equal to zero, data will be missed. The structure is excited by striking it with a calibrated dynamic impulse hammer. A force sensor mounted in the head of the hammer transforms the input 18

19 2.4 Rayleigh damping 19 force pulse into an analogous signal. A 2 channel FFT analyzer (Fast Fourier Transform) is used to compute the Transfer function/frfs (Frequency Response Function). In this experiment, Siglab post-processing modal software is used to determine the frequency response. Because accurate impact testing results depend on the skill of the experimentator, FRF measurements should be made with spectrum averaging, a standard capability in all modern FFT analyzers. For this experiment FRFs were measured using 5 impacts per measurement. The width of a resonance peak is a measure of the modal damping. The FRF amplitude of the system is obtained first. Corresponding to each natural frequency there is a peak in FRF amplitude. To estimate damping ratio from frequency domain, the half-power bandwidth method can be used. 3 db down from the peak there are two points corresponding to half power point, as shown in figure 2.8. The more damping, the more frequency range between these two points. Half-power bandwidth damping is defined as the ratio of the frequency range between the two half power points to the natural frequency at this mode. ω 2 ω 1 ω r = 2ξ r (2.16) in which ω 1 [Hz] = first half power point; ω 2 [Hz] = last half power point; ω r [Hz] = natural frequency; ξ r = damping ratio. Figure 2.7: Impact Testing Figure 2.8: Half-power bandwidth method (picture from machtool/machtool/vibration/ damping.html) Results Structural frequency response tests were done at three different PCB s, one PCB without any chip on it, one with one chip in the center position and another one with all 15 chips on it. The PCB is fixed according to the JEDEC standard (board level drop test method of components for handheld electronic products, JESD22-B111) on an aluminium plate using plastic standoffs. The aluminium plate is fixed and the accelerometer is fixed on the PCB. Each PCB is struck with the hammer at different places after that accelerometer 19

20 2.4 Rayleigh damping 20 locations are also changed. The frequency domain used in the experiment is 0-2 khz. The resulting frequency response functions are reproducible. To arrive at one set of Rayleigh parameters for each PCB, the experiments with different accelerometer and impact locations are averaged. In figure 2.9 a typical FRF can be seen. For calculation of the Rayleigh parameters modes at ±0 and ±1.2 khz are used, because consistent peaks were found at those frequencies. The coherence is used to evaluate the quality of each test. Figure 2.9: Typical frequency response function with two half power points The resulting Rayleigh parameters are mentioned in tables 2.3 and 2.4. Statistical analysis is done which shows that all parameters obtained have a standard deviation in the same order of the mean value, figure This tells that the values for α and β are not very reliable. The cause for this big standard deviation can be attributed to the fact that the PCB behaves very differently when struck at different locations. To improve the values the data is trimmed by replacing the lowest and highest 15% with interior points, this is called Winsor s theorem. Figure 2.10: Example of scatter plot of measurement data Figure 2.11: Example of scatter plot of measurement data 20

21 2.5 Simulation 21 α minimum α maximum α 0 chips chip chips Table 2.3: α and its boundaries for the different setups β minimum β maximum β 0 chips 2.18e e e-6 1 chip 2.01e e e-6 15 chips 2.47e e e-6 Table 2.4: β and its boundaries for the different setups The resulting dimensionless damping ratio as a function of eigenfrequency can be found in figure 2.11 which is an adaptation of the graph in figure 2.6. Shown are the values for a PCB without packages. 2.5 Simulation There are several ways to simulate an impact in MSC Marc/Mentat. For example it is possible to calculate the speed just before impact and use this to make the PCB fall on something using the contact tool. When the PCB falls down in this simulation it will crash on some points and bounce up again to come down a fraction of a second later. In the Philips experiments, as stated by JEDEC, due to a braking system, the PCB will only crash once. An other possibility is to fix the model in some points and prescribe the calculated velocity for the rest of the model. It is also possible to make use of the force or acceleration of the impact just as done in the paper STMicroelectronics [1]. At the Eindhoven University of Technology there is no possibility to measure the high accelerations that occur in such stiff impacts. So there is no possibility to measure the acceleration in an experiment and implement them into a model. Because paper [1] can be used as a comparison in this report the acceleration method is used. The acceleration used in [1] is a bit simplified and used as input data. This acceleration diagram is comparable with an impact of a PCB from a height at 1.5 meter and is not particulary created to comply with the JEDEC standards. In figure 2.12 the acceleration as function of time is shown. In Marc/Mentat it is possible to apply such a diagram as a boundary condition. This acceleration is not applied to the whole model because the PCB is only mounted at the inside of the 4 holes in the corners. When the PCB falls, the screws in the holes will receive the acceleration as described before, the rest of the PCB will behave differently. Therefore, in the model only the nodes around the holes will get the prescribed acceleration. This is not the only boundary condition: the assumption is made that the screws to mount the PCB are much stiffer then the PCB material. Therefore the screws will not deform at the impact. When the screws fall down straight, the nodes connected to the screws can only move in the z-direction. This is the second boundary condition for the model. 21

22 2.5 Simulation 22 The analysis is dynamic transient which is used to solve differential equations like M ẍ + C ẋ + Kx = f (t) (2.17) This is also called initial value problem. One could expect that an impact takes place during a small timespan so the analysis time is set to 0.1 seconds. For this analysis an initial speed is needed. Because acceleration is used as input and the PCB is in rest, the initial speed is set to 0. 4 x acceleration (m/s 2 ) time (seconds) Figure 2.12: Acceleration of the impact as described in paper [1] 22

23 Chapter 3 Validation The validation of the models made in Marc/Mentat will be done by comparison with results from the paper of STMicroelectronics [1] and experimental results gained by Philips. In [1], output acceleration is measured at the center of the PCB, as shown in figure 3.1. The model used is in [1] a model without microchips, sizes used are 100x48x1.6mm. This is roughly half the length and width of the modeled plate, but the plate in [1] is thicker. Acceleration in [1] is given in g-forces so to get acceleration in m/s 2 as used in the model, these values have to be multiplied with In figure 3.2 the output acceleration at the center of the PCB, modeled in Marc/Mentat is plotted. In the graph of figure 3.1 we can observe about 9 periods in 20 ms. The graph in figure 3.2 shows about 4 periods in 20 ms. So the cycle time of the model in this report is larger than in the article. From this difference it can be concluded that the stiffness of our model is probably too low, as predicted by the formula: ω = k/m. The ω is calculated with the formula 2π T so the ω from the model is twice as small as the ω from the experiment of the paper [1]. Now the density and volume are used to calculate the mass. Assuming that the densities are the same, the ratio between both masses will also be the same. If the density is 1 kg/m 3 the calculated masses become: 7.68e-6 kg for the experiment and 10.11e-6 kg for the model. Now these masses are used to calculate the stiffness. The outcome of this calculation shows that the stiffness of the model has a three times smaller value for k out of the paper. Most likely this is caused by the dimension difference of the models. Next, model results are compared to experimental results from Philips, being the acceleration of the jig and the center of the PCB. The measured acceleration of the jig and the center of the PCB is respectively shown in figure 3.3 and figure 3.4. The size of this PCB is the same as modeled in Marc/Mentat. Experiments were done with a PCB without packages. In the model without packages the acceleration on the jig (figure 3.3) is prescribed. This acceleration is in g-forces again and is converted to m/s 2 for the model. Because it is assumed that the jig is rigid compared to the PCB, the acceleration of the supports for the PCB will be the same as measured on the jig. This impact is simulated and the acceleration at the center of the PCB is determined. The acceleration data received from Philips (figure 3.4) is compared with the acceleration on the midpoint of the PCB during simulation (figure 3.5). To make the comparison more efficient figure 3.6 shows a smaller region of figure 3.5. The time between the first and the third peak in the experiment carried out by Philips is around 8 ms. For simulation results, 23

24 Validation 24 Figure 3.1: Acceleration (g) measured at the center of the PCB in the article [1] 5 x 104 Acceleration (m/s 2 ) at the center of the PCB with impact function of the paper [1] Acceleration [m/s 2 ] Time [s] Figure 3.2: Acceleration (m/s 2 ) at the center of the PCB as modeled with the impact function of paper [1] almost the same value is found for the time between the first and the third peak. In other words, the frequency of the vibration is almost the same for the experiment and the model. This also implies that the proportion between mass and stiffness for the experiments and the model agrees as well. This can be shown with the formula ω = k/m, which is already mentioned at the begin of this chapter. The height of the peaks are not the same in both graphs (figure 3.4 and figure 3.5), damping 24

25 Validation Acceleration (m/s 2 ) of the jig measured at Philips a (m/s 2 ) t (ms) x 10 3 Figure 3.3: Acceleration (m/s 2 ) of the jig measured at Philips, this is the input for the model does not differ much. The maximum acceleration of the midpoint in the experiment is 3.5e4 m/s 2 and in the simulation the maximum acceleration has a value of 1.7e4 m/s 2. It is hard to find an explanation for this huge difference; if no damping at all is considered in the model, the maximum acceleration in the midpoint will only be a bit higher (1.8e4 m/s 2 ), so the damping does not have much influence on the maximum acceleration. Also the effect of the impact duration on the maximum acceleration is explored. If the impact acceleration as shown in figure 3.3 is given in as a half sine it is easy to change the impact duration. In figure 3.7 the maximum acceleration of the midpoint is plotted against the impact duration. The points are approximated with a third order polyfit, as shown in 3.7. This fit is not ideal, but it does describe the tendency of graph. When a comparison is made between figure 3.8 and 3.9, an interesting phenomenon can be seen. With the increasing of the impact duration, the higher frequencies have disappeared in the response (as shown in figure 3.9). The descending of the points after 3 ms can be explained with the fact that the last bit of input acceleration does not help the maximum acceleration anymore, because the maximum acceleration is located before 2.5 ms. According to the polynomial approximation, the maximum acceleration of the midpoint can be 3.2e4 m/s 2 with an input peak duration of 2.8 ms. This is close to the outcome of Philips. Keep in mind that the duration stated by JEDEC [2], is only 0.5 ms. Furthermore it is questionable if an acceleration peak of 2.8 ms can still be considered as an impact. Despite all those facts, the conclusion can be made that the impact duration is of great influence to the maximum acceleration of the midpoint. 25

26 Validation 26 4 x 104 Acceleration (m/s 2 ) of the PCB center measured at Philips a (m/s 2 ) t (ms) Figure 3.4: Acceleration (m/s 2 ) measured at the PCB center by Philips 26

27 Validation 27 x 10 4 Acceleration of the midpoint in Z direction with impact of Philips with damping Z acceleration of the midpoint [m/s 2 ] Time [s] Figure 3.5: Acceleration (m/s 2 ) at the center of the PCB 2 x 104 Acceleration of the midpoint in Z direction with impact of Philips with damping 1.5 Z acceleration of the midpoint [m/s 2 ] Time [s] Figure 3.6: Zoomed in acceleration (m/s 2 ) at the center of the PCB 27

28 Validation x 104 Duration of the impact vs. maximum acceleration of the midpoint 3 Maximum acceleration of the midpoint (m/s 2 ) Simulation outcome Polyfit of 3th order Impact duration [s] x 10 3 Figure 3.7: Maximum peak height as function of the impact duration 2.5 x 104 Acceleration of the midpoint in Z direction with impact duration of s 2 Acceleration of the midpoint Impactfunction 1.5 Z acceleration of the midpoint [m/s 2 ] Time [s] Figure 3.8: Acceleration in z-direction at PCB center with an impact duration of 1 ms 28

29 Validation 29 3 x 104 Acceleration of the midpoint in Z direction with impact duration of s Acceleration of the midpoint Impactfunction 2 Z acceleration of the midpoint [m/s 2 ] Time [s] Figure 3.9: Acceleration in z-direction at PCB center with an impact duration of 1.5 ms 29

30 Validation 30 The damping ratio in the experiment of Philips and in simulation is more or less the same. In the experiment the first peak has a value of 3.5e4 m/s 2 and the third peak has a value of 2.4e4 m/s 2. The ratio between these peaks is In the simulation the ratio between the first and third peak is A smaller ratio corresponds to stronger damping. Because the α and β are determined with several experiments it is usefull to look around the averages. Therefor Rayleigh damping parameters α and β will be changed to see the difference in damping. To compare the results for different α and β values the ratio between the first and third peak is used. To get a feeling for the influence of α and β in the model these variables are changed independent of each other. Large variation of α and β are carried out, up to 30% lower and higher than the initial values. Results are presented in figure 3.10, from this figure can be seen that α and β have a similar influence on the damping ratio. Although damping ratio does not change a lot when α or β are largely varied, the damping ratio of Philips can be reached by increasing α with 13% or β 14.5%. After the changes in Rayleigh damping parameters, they are set back to the original values. The β dependency of the damping ratio of the midpoint of the PCB Simulation point for α fit through simulationpoints of α Simulation point for β fit through simulationpoints of β Damping ratio Percentage of original values Figure 3.10: Damping ratio as function of fraction of the original α and β next step is to explore the effect of changing the values for the mass and the stiffness in the model. This step seems logical, because this is the other part that influences the damping according to the formula C = αm + βk. Also M and K are approximations of the real values of the PCB. The ratio between the values of the mass and the stiffness has to be equal to the original value, otherwise the frequency of vibration will change. After a closer 30

31 Validation 31 look, it seems that these changes do not make any difference in the damping due to an obvious reason. The simulation of the impact is the solution of the equation: M ẍ + C ẋ + Kx = f (t) (3.1) f (t) is zero because no forces are given in. The input acceleration is in ẍ. And by changing C in αm + βk the resulting formula is: M ẍ + (αm + βk) ẋ + Kx = 0 (3.2) Now the change in M and K could be implemented as a factor f m before M and f k before K f m M + (αf m M + βf k K) + f k = (3.3) ẍ ẋ Kx 0 To get the same frequency of vibration the ratio between M and K should be the same, therefore f m and f k need to be the same. Then it is possible to split this up which results in: f[m + (αm + βk) + Kx ] = (3.4) ẍ ẋ 0 Now it is easy to see that changing f does not make any difference. The next step is to compare the eigenfrequencies of the numerical model with the eigenfrequencies found in the experiment. In figure 3.11, data of some of the dynamical experiments on PCB s is plotted along with vertical lines showing the frequencies of the eigenmodes as calculated by Marc/Mentat over a range from 0 to 2000 Hz. In this way, the dynamical response of the modeled PCB can be compared with the responde of the actual PCB. It can be seen that the lowest frequency found in the model at Hz, which largely determines its behavior, was indeed also found in all dynamical experiments. In Marc/Mentat, this mode corresponds with a simple bending of the PCB over its longest sides, shown in figure This gives rise to discussion: the mode depicted in the figure has the lowest frequency one could expect for this system. This is because every other mode will have a shorter wavelength than this one, and for the frequency goes: f = c λ with c the wavespeed in the material and λ the wavelength. However, in all experiments a very distinct peak in the frequency response plot is found at approximately 170 Hz, which is lower than the Hz for the first eigenmode found through simulation. Because the geometry of the model and the actual PCB is the same, the wavelength for the first mode calculated by Marc/Mentat and found by measurements, will be the same. This means that the wavespeed in the model is higher than in the actual PCB. This can be caused by using wrong material properties, but more likely by the simplification of the layered structure containing copper connections of the PCB. Thus bearing in mind that the lowest eigenfrequency calculated by Marc/Mentat, should coincide with the first peak in the measured frequency response plots, also the other frequencies calculated by Marc/Mentat are probably too high. This means that the peaks and frequencies that seem to correspond in figure 3.11, do this by pure coincidence. When the frequency response measurements are again plotted along with the frequency calculated by Marc/Mentat, but now with these frequencies multiplied by a factor of 170Hz/278.8Hz=0.61 to let the first modes coincide and to take into account the different wavespeed, this renders figure

32 Validation 32 Again, some peaks in the frequency response and modes calculated by Marc/Mentat coincide and at first glance this comparison seems to be nor worse nor better than the one made before. However, in the original comparison, some distinct peaks in the measured response did not coincide with any mode calculated by Marc/Mentat at all, whereas this now is the case. One could attribute this to the fact that now more eigenfrequencies predicted by the model lie in the interesting range below 800 Hz, but it is possible tot link the behavior of the measured response to the modeled eigenmodes. Of course, the first peak in the measured response now coincides with the lowest calculated eigenfrequency, due to the chosen calculation factor. The second calculated eigenmode now seems to correspond with the system around 280 Hz, where a resonance peak and a antiresonance peak can be found. The third interesting structure in the measured response is the region just above 400 Hz, where for different experiments different peaks can be found. The fact that not one distinct frequencies for these peaks is found might be due to the fact that there are more than one eigenmodes to be found there, as is predicted by the two calculated eigenfrequencies in that region. At approximately 600 Hz, again a distinct peak was found in most of the experiments, which also roughly coincides with a calculated eigenfrequency. At around 700 Hz, again a similar structure as just above 400 Hz can be seen, again accompanied by two calculated eigenfrequencies. This also is the case around 1000 Hz, but at higher frequencies, measurement begin to diverge significantly from each other and not much can be said about that regime in a sensible way. So, from these comparisons it could be concluded that, although the frequencies of the eigenmodes in the model are approximately a factor of 1/0.61 to high, the model does indeed seem to predict the lower eigenmodes. However, the sheer density of measured peaks and calculated eigenfrequencies might show a correspondence which does not have to exist, but are only there in the eye of the beholder. Therefore, these conclusions should be regarded with some suspicion. So it seems that the model as presented in this report is not accurate. This is because of the many simplifications that are made. Knowing the limitations of the model, useful features of the model can be explored. 32

33 Validation Comparisson of eigenfrequencies calculated by Marc/Mentat and measurements 10 3 Magnitude [ ] Modes calculated by Marc/Mentat chip00.s01h11.meting2 chip00.s01h11.meting1 chip00.s10h01.meting2 chip00.s10h01.meting1 chip00.s11h06.meting2 chip00.s11h06.meting Frequency [Hz] Figure 3.11: Comparison of eigenfrequencies calculated by Marc/Mentat and measurements Figure 3.12: First Eigenmode 33

34 Validation Comparisson of shifted eigenfrequencies calculated by Marc/Mentat and measurements Modes calculated with Marc/Mentat chip00.s01h11.meting2 chip00.s01h11.meting1 chip00.s10h01.meting2 chip00.s10h01.meting1 chip00.s11h06.meting2 chip00.s11h06.meting Magnitude [ ] Frequency [Hz] Figure 3.13: Comparison of shifted eigenfrequencies by Marc/Mentat and measurements 34

35 Chapter 4 Model possibilities By implementing the PCB in Marc/Mentat many other results can be obtained. Not only the acceleration, displacement and velocity can be found but also values for stress and strain. In real experiments it is hard to measure these strains and even impossible to measure the stresses without modifying the PCB. By using a model it is possible to calculate the stresses and strains and gain lots of information about it. In this chapter some examples will be given of what is possible with the Marc/Mentat model. For this chapter the model of the PCB with the 15 chips is used. In chapter 3 the validation is done with the PCB without chips, because this was the only possible comparison. However, to give some more detail here the model with 15 chips is used. 7 x 106 Stress of midpoint PCB with impact of m/s 2 Stress in point 136 Stress in point Stress of the midpoint [Pa] Time [s] Figure 4.1: Equivalent Von Mises stress at the center of the PCB with impact acceleration of m/s 2 In figure 4.1 an example is given of the equivalent Von Mises stress at the centerpoint of the PCB, point 136, and at the center of the microchip above the center of the PCB, point The graphs differ only a little bit this is because nodes are tied together as shown in 35