Hot Isostatic Pressing

Hot isostatic pressing (HIP) modeling is based on a phenomenological constitutive relation for powder consolidation under high pressure and high temperature. The consolidation of metal powders via HIP can produce cost-effective, high-quality, and high-performance components. The advantages of HIP processing over casting include a uniform, fine grain structure without shrinkage porosity, inclusions, and segregation; a decrease in machining time due to making parts nearer to net shape and with a finer microstructure; and reduced residual stresses that can cause parts to undergo distortions during finish machining. In spite of these advantages, the cost-effective manufacture of parts with complex shapes via HIP has been hindered by difficulties in achieving suitable dimensional control.

Currently, the containers that hold the powder and define the component shape are designed by trial and error; this is very costly and time consuming. In each iteration, the container is redesigned and another part is HIPed to determine the effect of the design modification. Depending on part size and alloy, the cost can exceed $100,000 per trial (1998 dollars), and each iteration can take months to complete. To reduce costs associated with shape control by trial and error, it is necessary to accurately predict the final shape of the as-HIPed component during the design stage.

With computer models that accurately predict the as-HIPed shapes, simulations may replace actual HIP trials, thereby reducing the expense of container design and the lead times for new components. Using a computer model, a container design iteration could be measured in days or weeks rather than months, and the cost of actual HIP trials would be saved.

General Conditions of HIP Modeling. The HIP methods is essentially a thermomechanical process. In HIP, powder consolidation and heat transfer occur simultaneously. The physical mechanisms involved in the powder consolidation include plastic yielding, creep, and diffusion. The local stress and temperature in the powder compact govern the contribution of these mechanisms to the powder consolidation. Heat transfer (mainly heat conduction) in the powder compact is strongly influenced by the local relative density. Therefore, the analysis of HIP is a coupled thermomechanical analysis.

Modeling the HIP process requires the solution of a boundary value problem described by:

• Equation of motion

• Conservation of mass/continuity equation

• A set of constitutive equations

• A proper set of initial and boundary conditions

To fully specify the constitutive model of the powder and can material, a variety of experiments should be performed. The testing approach and data analysis is described in the next section. Prior to discussing the constitutive model, it is also important to distinguish between the microscopic (powder particle) deformation associated with individual particles and the macroscopic (powder aggregate) deformation of the powder aggregate idealized as a continuum. At the macroscopic level, field variables such as stress and strain are defined over a small representative material element containing enough particles to qualify for a macroscopic regime. Clearly, an exact solution of these field variables would require the solution of a boundary value problem involving the exact number, shape, and size of these particles. At the microscopic level, the field variables of each particle are obtained in some average sense. Thus, the particle quantities are defined as those obtained by averaging the actual particle values (obtained from the unified theories of dislocation driven plasticity for isotropic materials) over the macroscopic material element. These two modes of deformation, which constitute the basic philosophy of the proposed methodology, facilitate the tracking of internal state evolution of the material as a whole and the individual particles in some average sense. Details of the development of the viscoplastic constitutive model for the densification of metal powders during HIP have been reported previously (Ref 19, 20). Additional information is also contained in the article "Principles and Process Modeling of Higher Density Consolidation" in this Volume.

Constitutive Model. Power-law creep represents the flow behavior of the container material. The flow behavior of the powder is represented as a combination of the particle flow behavior and the powder aggregate flow behavior described by the following macroscopic, viscoplastic potential function or yield function, ^(Ref 19, 20). This function represents the evolution of yield loci as a function of relative density:

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