Simulation of Thermally Activated Metal Forming Process With Meso-Scale Crystal Plasticity

Under thermally activated deformation conditions many engineering metals (steels, aluminum and magnesium alloys) exhibit much enhanced formability; thus, thermal forming has received increasing interests by automotive industries. The thermally activated material constitutive behaviors are not only strain dependent, but also strain rate and temperature dependent, and it is sensitive to in-situ microstructure evolution. In addition, non-steady-state deformation at a high strain rate (in the order of 10−2s−1 or above) introduces additional challenges in forming simulation. In this case, von Mises based macroscopic plasticity are often not sufficient to describe material behaviors with complex thermomechanical history. In this paper, the rate-dependent crystal plasticity model [1] was applied to the high temperature and high strain rate deformation that is dominated by dislocation creep. A user material subroutine was developed and used for FEA metal forming simulation using commercial ABAQUS/Dynamic code. In the simulation, material behavior was computed based on crystal plasticity at each strain increment without using von-Mises equation or a look-up table of material testing data. By inputting different slip systems or their combinations, and by matching the predicted crystallographic textures with experimentally obtained ones, the active slip systems responsible for the deformation was identified. Then, the material parameters were best fitted to the tensile curves obtained at various strain rates and temperatures. The model was applied for more complex multi-axial metal forming processes. The material behavior, along with its crystallographic texture development, was obtained and validated. As a demonstration, this paper also provides an analysis of a newly developed thrmal forming process [2] with this meso-scale crystal plasticity approach. This forming process involves diameter expansion of a tubular workpiece under combined internal pressure and axial loading and at elevated temperatures.

A Damage Identification Method Using Vibration Modal Parameters Through Finite Element Discretization

Natural frequencies and mode shapes of a structure will change whenever the structure has any kind of damage. This paper introduces a technique to quantify and locate the damage when the natural frequencies and mode shapes of undamaged and damaged structure are known. Aluminum beams (with and without damage) are used for numerical simulation and experimental verification. To establish the theoretical basis of this method, finite element formulation is used. A set of undetermined equations involving damage indices and natural frequencies and mode shapes of undamaged and damaged structures are obtained. The damage indices are computed using non-negative least squares method. Impact modal testing was conducted with three aluminum beams and damage indices based on experimental data are compared with actual damage cases to establish the effectiveness of this method to identify the damage.

Impulsive Forming of Shell Structures With Apertures

Different modern shell structures are exposed to impulsive loading very often. Some of them may have different imperfections such as apertures, welds, and irregular thickness. These structures can be made by static or impulsive loading. To know fractureless dynamic response of shell structures with apertures is important in many cases, especially for forming processes, because of the first appeared fracture can extend through a shell blank especially if material is brittle with low plastic properties. The tooling for impact and static loading of flat and shell structures was developed. Dynamic response of shell structures with unsupported apertures on internal impulsive loading by point high explosive charges is described. Strain state of shaped shell structures with apertures after explosive forming is shown. The limit aperture diameter for dynamic fractureless response is determined. Distributions of strain intensities on a sample cross section for different aperture diameters, static and dynamic loading are shown. Different jet engine parts were made using developed technology.

Shear Deformation of High Density Aluminum Honeycombs

The orthotropic crush model has commonly been used to describe the constitutive behavior of honeycomb [1]. To completely define the model parameters of a honeycomb, experimental data of axial crushes in T, L, and W principal directions as well as shear stress-strain curves in TL, TW, and LW planes are required. The axial crushes of high-density aluminum honeycombs, e.g., 38 pcf (pound per cubic foot), under various loading speeds and temperatures have been investigated and reported [2]. This paper describes experiments and model simulations of the shear deformation of the same high-density aluminum honeycomb. Results of plate shear test, beam flexure test, and off-axis compression are presented and discussed.

Opportunities and Challenges in Mesoforming

In the last ten years, miniaturization technologies have revolutionized product design and have lead to many innovative applications in the automotive industry, healthcare, environmental monitoring, industrial processing, energy consumption, defense, etc. Here, the current state-of-the-art in mesoforming (forming of metals in the scale of 0.1 mm to several millimeters) is reviewed, followed by our preliminary investigation of one mesoforming example.

Multiscale Modeling of Large Deformation Processes in Polycrystalline Metals

A mesoscale model for predicting the evolution of the grain structure and the mechanical response of polycrystalline aggregates subject to large deformations, such as arise in bulk metal forming processes, is presented. The gain structures modeled are either experimentally observed or are computer generated and statistically similar to experimentally observed grain structures. In order to capture the inhomogeneous deformations and the resulting grain structure characteristics, a discretized model at the mesoscale is used. This work focuses on Al-Mg-Si alloys. Scale bridging is used to link to the macroscale. Examples involving two-dimensional grain structures and current work on three-dimensional grain structures are presented. The present work provides a framework to model the mesoscopic behavior and interactions between grains during finite strains. The mesoscale is characterized by a statistically representative voluem element (RVE), which contains the grains of a polycrystal. Experimentally observed grain structures are used both as models directly (for two-dimensional cases) and to define statistical characteristics to verify the similarity of computer generated grain structures (for three-dimensional cases). A Monte Carlo method based on the Potts model is used to define three-dimensional grain structures. In order to make the representative grain structure appropriate for scale-bridging, we design them with periodicity. A three-field, updated Lagrangian finite element formulation with a kinematic split of the deformation gradient into volume preserving and volumetric parts is used to create a stable finite element method in the context of nearly incompressible behavior. A fully implicit two-level backward Euler integration scheme is derived for integrating the constitutive equations, and consistent linearization is used in Newton’s method to solve the resulting equations. In addition, the average of the boundary conditions and bulk response must match the macroscopically measured bulk response. To illustrate and verify the proposed model, we analyze examples involving two-dimensional grain structures and compare with results from a Taylor model. Current work on three-dimensional grain structures ara also presented.

Nonlinear and Chaotic Vibration-Based Damage Detection

The dynamics of an aeroelastic system composed of a panel forced by unsteady buffeting aerodynamic loads is investigated numerically. The focus is on detecting parametric changes in the system. The upstream end point of the panel is considered supported by a spring of variable stiffness. Changes of in the stiffness of the spring are detected by exploring the chaotic dynamics of the panel.

Short Crack Growth Model in a Particulate Composite Using Nonlinear Elastic Fracture Mechanics

The fracture mechanics model for a long crack does not work very well with short-crack propagation when the initial crack length is less than 5.1 mm (0.2 inch). In order to investigate the short crack effect, a series of tests of particulate composite specimens with long and short cracks were performed and the results recorded on a video tape. This test data was analyzed to determine the fracture parameters. Two initial crack lengths, 2.5 mm (0.1 inches) and 7.6 mm (0.3 inches) were used in the crack propagation tests. Based on the principle of linear elastic fracture mechanics (LEFM), the stress intensity factor KI was obtained. The instantaneous time-dependent J-integral for 0.1 and 0.3 inch crack specimens was determined by the NEFM analytical approach. The crack growth behavior was also investigated in the form of J-integral resistance curves. The calculated J-integral was reversed to derive a new KI. The new KI was compared with the measured value obtained from LEFM analysis results to determine the feasibility of applying the linear fracture approach to the non-linear behavior of the material. The results showed that the KI computed from the J-integral increased by 24.5%, and was at the time prior to the peak load for the 0.1 inch crack. For the 0.3 inch crack, the acceptable range was from the onset of propagation to the 9% strain stage (yield strain for the material), where the increase of the new KI was within 15.6%.

Preliminary Investigations of a High Temperature Cu-13.3%Al-4%Ni Shape Memory Alloy Single Crystal

Preliminary investigations on the constitutive response of a Cu-13.3%Al-4%Ni (wt%) shape memory alloy single crystal with stress-free transformation temperatures around 100 to 150°C are reported. Room temperature stress cycling tests were carried out at very low deformation rates. Reproducible stress/strain curves of up to 9% strain due to detwinning (martensitematensite phase transformations) with no plastic deformation were obtained. The data also indicated that a period of stress cycling is required to stabilize the material before reproducible stress-strain curves are obtained due to martensite reorientation.

Modeling of Metallic Sandwich Structures

All-metal sandwich construction holds promise for significant improvements in stiffness, strength and blast resistance for built-up plate structures. Analysis of the performance of sandwich plates under various loads, static and dynamic, requires modeling of face sheets and core with some fidelity. While it is possible to model full geometric details of the core for a few selected problems, this is unrealistic for larger complex structures under general loadings. A constitutive model can be proposed as an alternative means of modeling the sandwich core. The constitutive model falls within the framework of a compressible rate-independent, anisotropic elastic-plastic solid. In this paper, the model will be presented in details, along with numerical implementation in a finite element code, and benchmarks its performance against existing constitutive models.