Abaqus simple case 2: indentation of thin coating

vickers schemaThis is my second post in step-by-step modeling process using ABAQUS. Abaqus’s feature which is very challenging but also interesting is contact-interaction. This feature is very powerful for any engineers who are working in product development or in predicting materials behavior under certain circumstances.

Since my background study is in surface treatment, I take coating indentation as my case study. We only consider half part in this simulation because the model is symmetric. The element type of both coating and substrate are CAX4R (A 4-node bilinear axisymmetric quadrilateral, reduced integration, hourglass control) with first-order accuracy. First-order accuracy is used due to its less sensitivity and it is a better choice when mesh distortion is expected. However, second-order elements clearly outperform first-order elements in problems with stress concentrations and are ideally suited for the analysis of cracks.

Suppose that we have two different coating materials; copper representing ductile material and mullite representing brittle material, which are deposited on AINSI steel 304L. (You can change it with alumina, silica, zirconia or other ceramic materials). We assume there is smooth and frictionless between the Vickers indentor and the coated materials. We would like to know the different damage shape of ductile and brittle coating and shear stress distribution (S12) underneath of interface. We also want to predict where the crack will be initiated.

To simplify the problem, I do not include cohesive behavior and crack propagation. It is because the  material properties of interface between mullite-steel or alumina-steel supporting this theory is unavailable. Too many assumptions are taken to model cohesive-behavior in this case so it is better to leave it for while. Tough, it is one of the most researched field in fracture mechanic science. Cohesive theories describe the evolution of a fracture as the progressive separation of two surfaces. The separation is described by the displacement jump between two points, originally coincident, on the two cohesive surfaces. I’ll demonstrate the application of cohesive behavior in crack initiation using ABAQUS in the next posting.

The modeling algorithm of coating indentation can be summarized as follow :

  1. Indentor as rigid body constraint so it is not deformable. Create model as 2D deformable axisymmetric plane. The indentor created with 2D planar will not penetrate the substrate.
  2. There is interaction among the surfaces and the coating is well adhered on steel substrate by using tie-constraint.
  3. Indentor will penetrate by adjusting displacement in vertical direction (-y) on Boundary Conditions Manager.
  4. Create good mesh to avoid excessive distortion. When the indentor penetrates onto the substrate, ABAQUS will discretize the element movement based on node to surface or surface to surface between indentor and coating & substrate. This is why the mesh of Slave (coating & substrate) should be finer than Master (indentor) surface. Ensure that every nodes in the coating, interface and substrate are well aligned. This is also important to have converged result, otherwise we will get error too many increments needed to complete the step.

The main use of principal stress is to predict failure in a structure which has a complex state of biaxial or triaxial stress. The use of maximum principle stress is more accurate for brittle materials while von Mises criterion is preferable for ductile materials. As we can see from this animation, maximum plane stress is generated underneath of the tip. Tough, this result is not validated yet with experimental design. I have been thinking to compare it with the stress and damage resulted from cohesive-behavior.

Maximum plane stress animation of brittle coating material (mullite)

Maximum shear stress S12 animation of brittle coating material (mullite)

Based on the stress localization, we can determine where it might fail. Now, i am curious to see what happen if I change mullite with such a ductile material. So, I decided to use copper and change the material properties. Here, there is a little bit different damage shape and the position of stress localization.

  Maximum shear stress S12 animation of ductile coating material (copper)

Further investigation are still needed to investigate where crack will initiate. However,  S12 (maximum shear stress) value along the edge path shows that crack will not be initiated underneath of indentor tip but it might be slightly deviated from the tip.

create path using edge list and view result s11

s12 component along path

Details of modeling process :

1. Create part, materials, assign sections and instance. This is the basic process of modeling. If you are not familiar with this step, it is recommended to watch tutorial of beam modeling using Abaqus on youtube (So far, that is one of the easiest example I can find). Define surfaces of each part which will be involved in interactions by clicking part directly from tree menu.

2. Create interaction properties and set tangential behavior as frictionless since we assume there is no friction between indentor and surface. Name it as “touch”

3. Create contact using interaction module. In this case, there are two possible of contact interactions. First, the indenter will touch the exterior nodes of coating and transfer the load by pushing them. So, choose general contact, select all surfaces, select contact property “touch” and set the default.  The second contact interaction is between coating and substrate. Since the coating is strongly adhered on the surface, create surface-to-surface contact interaction and make tie-constraint as shown on the following screenshoot.

create surface interactions

5. Create constraints. By clicking directly on the tree menu, create rigid-constraint and select reference point of displacement. This point will be used as a reference of indentor’s movement. Using the same technique, create tie-constraint and select the bottom surface of coating and top surface of substrate, so those surfaces will be strongly adhered.

6. Create boundary conditions as shown in the following figure. Bottom surface of substrate is encastred while edge is pinned. To make vertical movement of indentor, tick displacement/rotation and set U2 = … (for example U2 = 0.05). The magnitude of displacement should be rational value and consistent with the units that we have defined on the previous step, otherwise the calculation will not converge.

boundary conditions

7. The criteria of good mesh is not clear. In general, regions which are predicted to show large deformation should have high mesh density to obtain more accurate result. In contact interaction case, it is recommended that slave surface is finer than master surface. Nodes alignment of unconnected regions as seen on the following figure dashed in red line(interface between coating and substrate) will also determine the load transfer and thus the convergence of our simulation.


Hope you learn something 🙂

PS : Thank you for reading my blog. Since I received many comments asking for Abaqus files and i always respond it lately, here I attach the download link. You can also send me an email if this link does not work.


ABAQUS simple case 1: reservoir filled with pressurized liquid

If we read ABAQUS manuals, we can find a lot of case studies and instruction explaining how to analysis a model. Beam and truss analysis are the most popular examples used in university because of its easiness and simplicity. If you are not familiar with ABAQUS features, please read it first on internet. However, ABAQUS manual does not provide the step-by-step instruction for pieces with complex shape and interaction. This is the reason I write this blog. I just want what I have learned in my class.

Please keep in mind that ABAQUS is a general Advance Finite Element (FE) tools to solve wide variety and complex problems. It is just a “tool” which helps up to solve the problem but we are the one who are responsible for defining the problem. The validity of our result strongly depends on how we understand and define the physical model. It is differed from SAP2000 or other “specialized” FE software in civil engineering. As consequence, it needs special care and little bit imagination. The most powerful feature in ABAQUS is its calculation capacity to address linear or non linear physical behavior, not in design like other CAD softwares such as AutoCAD, Catia, Solidwork, etc. So, try to simplify the design if it is possible.

Suppose that we have a simple 3D reservoir having wall thickness 5 mm, encastred on its neck, weight applied and under pressure from liquid which fill all spaces. It is made of cast iron which is a brittle virtually non-maleable metal that is considered generally inflexible. The mechanical properties are shown below :

E = 210.E9  Pa                         ν = 0.3                            ρ = 7100 kg/m³

Calculate and find the position where stress concentration is maximum?

model of simple reservoir filled with pressurized liquid

The following description are step by step processing using ABAQUS student version 6-12.2. In this tutorial, I will not go into details, please read manual instruction of ABAQUS for further details.

1. Create Model (part, material property). The model was created by revolving 3D, deformable shell. Please see “getting started with Abaqus”

2. Define step, load and boundaries condition. The inital state of our reservoir is empty. Before fluid filling, there is only gravity force applied on the body. When we inject the fluid, uniform pressure applied on the body. So there are three main steps as seen on the above schema. Apply pressure in the load module and encastrement on the neck as seen on the following schema.

define pressure for liquid and internal faceencastred1

3. Create Seed, mesh and mesh verification. The result accuracy depends on the mesh quality such as density, uniformity, shape ratio, angle variations, etc. In this model, we used seed edge and swept meshing.

There is no fixed rules of meshing according to manual instruction of ABAQUS but the regions which might have large deformation should have high mesh density. It is recommended to use hexagonal, quadratic elements (all element ends with “4” such as CPE4, CPE4T, DC2D4) instead of trilingual element (all element ends with “3” such as CPS3, CPE3T, DC2D3) to ensure convergence value. The element selection depends strongly on the physical  phenomena works in the model. The element we use for heat transfer or thermo-mechanical problems will be different for contact or stress analysis. Please see manuals for further details of the choice of elements. Since the wall thickness is thin enough compared to the whole size, we assume that plane stress is applied, thus CPS4 element is used.

Distorted element will lead to non-convergence value and it can be very frustrating, so please use mesh verification, edit and control if it is necessary.

before mesh improvement - swept meshing after mesh improvement - swept meshing

 mesh improvement of neck-front surface using swept mesh

before mesh improvement - mesh control using face curvature after mesh improvement - mesh control using face curvature

mesh improvement using face curvature control

4. Define F-output, job submission and view result.

view result along path

If we want to view stress value along the certain point or path, we can use edit note list path from visualization Module


Von Mises distribution representing the location of stress concentration

view deformed section

Deformed part and stress concentration

Hope you learn something, the next post will be in “contact” cases  🙂

PS :  This model is made using ABAQUS student version which has very limited nodes (maximum 1000 nodes). If you want to use complex shape, try to use other version. The more nodes you use, the more accurate is the result.

Download link :


Recent Development of High Temperature Materials For Application in “Waste to Energy” Plant


Waste is a big problem in Jakarta. This city produces approximately 30 – 37 thousand meter cubic or 7700 tons per day domestic waste which 15%  is unable to be collected and removed to the primary landfill. There is no reference detailing the percentage composition of degradable and non-degradable, but the important thing I want to highlight here is the absence of long term strategy to manage non-degradable waste. While in developed countries such as Canada, France and Sweden, the regional governments realize that the demand of waste management and waste incineration technology are urgent. Waste incinerator has an important role, not only to decompose non-degradable waste but also to convert it into heat energy which can be reused for electricity.

However, waste incineration technology is still posing a lot of technical problems due to corrosion phenomena. High Temperature Corrosion (HTC) in waste incinerator is caused by chlorine attack, in which its fundamental corrosion mechanism is not well understood. This mechanism is slightly different with that of HTC in gas turbine, diesel engine or furnace where corrosion is induced by the presence of hot gases containing Vanadium or Sulfates.

One of the leading research group which conduct extensive research in this field is Swedish High Temperature Corrosion group. I was lucky because I have visited this research group in Goteborg a year ago. Their laboratories are well equipped, having strong financial support from local renewable energy companies and they were really interested to my internship paper about HTC in incineration facility. This is the reason that I want to publish it so everyone can understand the recent problem and what are the primary concerns in the coating technique selection in waste incineration.


Waste management is in crisis in the world largest urban areas as the population of the cities continues to grow. This has led to the high demand of waste incineration which can accommodate the increasing of solid waste in very limited disposal space. The integration of waste incineration and energy recovery, well known as Waste to Energy (WTE) is believed to be beneficial since it offers not only volume reduction of waste (until 90%) adaptable to any kind of waste (municipal to biologic pollutant) but also releases combustion energy which can be transformed to heat and electricity form and eventually gas fuel.

Chlorine containing corrosion in high temperature is a challenge that crosscuts WTE industries and is considered as the worst condition in corrosion case. Some studies have shown that chlorine corrosion is a major problem in WTE and biomass-fired boiler since chlorine gaseous (560-2240 vppm) was dominant over other compound such as sulfur (100-2000 vppm). Chlorine concentration in fuel were 0.5% in average, or 5 times higher than that of coal power stations which allow them to be operated in higher temperature and thus have better efficiency (up to 33%).

In active oxidation, corrosion rate is appeared to be proportional to temperature, whereas reducing the temperature of steam is undesirable in reason of thermal efficiency. It is clear that the efficiency of plant is limited by corrosion resistance of materials. Therefore, coating method with special material was developed to obtain material which could withstand in very aggressive environment at high temperature. Some coating materials with certain deposition methods were successfully developed in laboratory scale but failed in industrial application or were not economically viable at large scale. Therefore, if some methods are promising, further investigations are still needed.

Heat transfer surfaces like waterwall, screen tubes and the superheater are the most sensitive areas attacked by corrosion. Heat exchanger (Waterwall) and superheater tube are very risky to chlorine corrosion attack in WTE due to the presence of chlorine containing deposit as explained on the following section.


The mechanism of chlorine corrosion attack is still debated. However, two well known mechanisms were proposed:

1. Corrosion due to active oxidation

It is possible that direct gaseous corrosion attack leading to active oxidation of metal substrate Fe2O3 which has spongy non protective surface. This reaction is also releasing Cl2 gaseous which may diffuse back into the surface and promote again the formation of volatile metal chlorides. However, some works confirmed that gaseous chlorine attack is less corrosive than alkali chloride condensed on superheater surface

2. Corrosion due to deposit by sulfation and molten salts

This corrosion mode is also known as fluxing mechanism since the product of this reaction may dissolve protective oxide scale and accelerate loss of coating when heavy-metal chlorides such as PbCl2, ZnCl2 present (see illustration below). Some publications suggested that only one mechanism is involved while others suggested that the mechanism of corrosion is a combination of both: direct gaseous attack and deposit by sulfation of molten salts. When the chlorinated gas penetrates and reaches the metal surface M, it will immediately react with M and forms an eutectic metal chloride M-Cl which is volatile below 900oC, while the temperature of flue gas on the surface may reach more than 850oC.

corrosion mechanism in WTE

corrosion mechanisme


Nowadays, the two main routes that are explored for fighting corrosion in WTE and more particularly in superheaters and heat exchangers are (i) the development of new corrosion-resistant alloys and composites that can withstand the high temperatures necessary to attain a high efficiency level and (ii) the development of corrosion-resistant coatings. This work focuses on the second route.  The substrate and coating materials characteristics are reviewed.

2.1 Substrate material

Superheater and heat exchanger are the most risky parts to corrosion attack in WTEs due to condensation of volatile metal chloride as already explained in section I. Important considerations for the selection of substrate material for superheaters and heat exchangers are thermal conductivity and material cost. Substrate materials should have high thermal conductivity as well as high corrosion resistance to perform well at high temperatures. Ferritic and austenitic steels are the most common metals used as substrate material. Experimental results showed that chromium content in typical ferritic steels 2.25 w.%t results in good conductive properties and low cost. While austenitic steels chromium contained higher amount of chromium (27 wt.%), nickel (31 wt.%) are more resistant to corrosion but less thermally conductive and also more expensive. In boiler design, austenitic steels are used only if ferritic steels cannot withstand the high temperatures of operation, the mechanical load or the corrosive environment.

2.2 Coating materials and methods

Theoretical specifications of coating which are described in details in this reference suggested that coatings should be thermodynamically stable, show minimum interdiffusion and their Coefficient of Thermal Expansion (CTE) should be as close as possible to that of substrate. However, there are two other additional specifications that should be considered as complementary factors.

1. Coating should show minimum dissolution induced by melting of metal chloride. In highly chlorinated environment like waste incineration, oxide dissolution that is is well known as fluxing mechanism is an initial step in corrosion mechanism. Fluxing is referred to dissolution of oxide layer that is protecting metal surface caused by deposit of low melting point salt. P.Viklund found that in ferrous alloys with Ni, Cr, Mo, the addition of Nickel and Molybdenum were beneficial even though they do not contribute to the formation of protective oxide scales but Ni may form NiO which is less soluble in chloride salt.

2. Coating should be thick enough with no interconnected porosity. If crack occurs on surface, thick coating may postpone the diffusion of corrosive substances until the underneath layer forms protective oxide, thus increasing lifetime of service.

According to the mechanism of corrosion described in section I, it is clear that permeability of protective oxide is responsible for all of corrosion attack modes. The direct chlorine gaseous attack and metal chloride cycle attack induced by the formation of metal chloride can be avoided if only the corrosive species are unable to penetrate and to reach the metal substrate. Thus, it can be concluded that coating should be designed as impermeable as possible by reducing interconnected porosity and by improving adherence between substrate and coating.

Various coating methods were developed and two types of coating can be generally distinguished: traditional plain coating composed by a single layer and multi layer coatings with an intermediate self healing barrier. Details of advantages and disadvantages of each techniques are resumed on the table below.

review of coating technique

review of coating techniques

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